Aim: The purpose of this study is to evaluate the Ottoman Empire's first experienced quarantine and the Turkey Republic's used compartmental models within quarantine. Method: This study was conducted as a review to explore quarantine procedures applied from Ottoman Empire to the present time in the Turkey Republic. For this purpose, we collected pieces of evidence from historical texts, articles, online reports, and books to websites. The reviews findings were assessed chronologically. Results: There were findings about the Ottoman Empire (...) and Turkish Republic. The first data was included in the quarantine directives of the Sultan II. Mahmud (1808-1839) for cholera. Moreover, the Ottoman Empire continued to fight epidemics such as the plague, cholera, smallpox, malaria, and Spanish flu. After founded, the Turkish Republic state (1923) has also encountered some infectious diseases (cholera, COVID-19) and used compartmental models within quarantine with medical measures. However, while quarantine applications were made more effective with technology, COVID-19 was held back with the old quarantine application principles at short intervals. On the other hand "compartmental models within quarantine" concepts and practices were carried out in many countries instead of only quarantine and after a while implicitly followed by many countries for economic reasons; this system was introduced, which caused controversy for economic reasons, including Turkey. Conclusion: Infectious diseases not only threaten the health of people but also threatens socio-economic life and even cultural and religious practices. For this reason, its area of influence covers a wider area, the world in all other disasters. In spite of all scientific and technological developments, infectious diseases can still not be brought under control in a short time and measures have started to evolve from quarantine, social distance practice, and herd immunity system. This study offers the opportunity to reconsider and think of quarantine practices from past to present. (shrink)

Tuberculosis has continued to retain its title as “the captain among these men of death”. This is evident as it is the leading cause of death globally from a single infectious agent. TB as it is fondly called has become a major threat to the achievement of the sustainable development goals (SDG) and hence require inputs from different research disciplines. This work presents a mathematical model of tuberculosis. A compartmental model of seven classes was used in the (...) model formulation comprising of the susceptible S, vaccinated V, exposed E, undiagnosed infectious I1, diagnosed infectious I2, treated T and recovered R. The stability analysis of the model was established as well as the condition for the model to undergo backward bifurcation. With the existence of backward bifurcation, keeping the basic reproduction number less than unity $$({R_{0}}<1)$$ is no more sufficient to keep TB out of the community. Hence, it is shown by the analysis that vaccination program, diagnosis and treatment helps to control the TB dynamics. In furtherance to that, it is shown that preference should be given to diagnosis over treatment as diagnosis precedes treatment. It is as well shown that at lower vaccination rate (0–20%), TB would still be endemic in the population. As such, high vaccination rate is required to send TB out of the community. (shrink)

Here, an epidemiological model considering pro and anti-vaccination groups is proposed and analyzed. In this model, susceptible individuals can migrate between these two groups due to the influence of false and true news about safety and efficacy of vaccines. From this model, written as a set of three ordinary differential equations, analytical expressions for the disease-free steady state, the endemic steady state, and the basic reproduction number are derived. It is analytically shown that low vaccination rate and (...) no influx to the pro-vaccination group have similar impacts on the long-term amount of infected individuals. Numerical simulations are performed with parameter values of the COVID-19 pandemic to illustrate the analytical results. The possible relevance of this work is discussed from a public health perspective. (shrink)

In this paper, we study a stochastic epidemic model with double epidemics which includes white noise and telegraph noise modeled by Markovian switching. Sufficient conditions for the extinction and persistence of the diseases are established. In the end, some numerical simulations are presented to demonstrate our analytical results.

This paper applies models of the onset of adolescent sexual intercourse using national data from Denmark and the USA. The model gave excellent fits to data on Danish Whites and a good fit to American Whites, but the model-fits for American Blacks and Hispanics were not as good. The weakness of the latter model fits may reflect either real processes that the model does not capture or problems in the reliability of adolescent sexuality data.

Modelling of contagious disease usually employs compartmental SEIR-like models where the waiting times in respective compartments are exponentially distributed. In this paper, we are interested in investigating how the distributions of sojourn times in infective compartments affect the dynamics and persistence of the contagious bovine pleuropneumonia, a chronic respiratory disease of cattle. Two kinds of extreme distributions of the sojourn times are considered: a Dirac delta-function and truncated Gaussian function leading to a model with (non-constant) delay and the (...) classical exponential distribution that stands for a model without delay. Expressions of the basic reproductive numbers are derived and dynamical behaviours are discussed for the three models. It is found that the spreading of disease exhibits wave-like oscillations for the time-delay dynamics. In contrast, the disease appears to last longer when the spreading is described by the classical dynamics without delay. Subsequently, the time-delay dynamics turns out to be more appropriate for the description of an experimental epidemic of CBPP. (shrink)

Whooping cough is a highly transmitted disease around the world. According to the World Health Organization, 0.15 million cases had reported globally in 2018. Most of the Asian and African states are infected regions. Through the study, we investigated the whole population into the four classes susceptible, exposed, infected, and vaccinated or recovered. The transmission dynamics of whooping cough disease are studied analytically and numerically. Analytical analyses are positivity, boundedness, reproduction number, equilibria, and local and global stabilities. In numerical analysis, (...) we developed an implicit numerical integration scheme consistent with the biological problem’s properties. The analysis of the implicit method for the said model is dynamically consistent, positive, and bounded. Furthermore, an implicit numerical integration scheme is suitable for studying a particular epidemic model such as the whooping cough disease. (shrink)

While most masks have a limited effect on personal protection, how effective are they for collective protection? How to enlighten the design of masks from the perspective of collective dynamics? In this paper, we assume three preferences in the population: never wearing a mask; wearing a mask if and only if infected; always wearing a mask. We study the epidemic transmission in an open system within the Susceptible-Infected-Recovered model framework. We use agent-based Monte Carlo simulation and mean-field differential (...) equations to investigate the model, respectively. Ternary heat maps show that wearing masks is always beneficial in curbing the spread of the epidemic. Based on the model, we investigate the potential implications of different mask designs from the perspective of collective dynamics. The results show that strengthening the filterability of the mask from the face to the outside is more effective in most parameter spaces because it acts on individuals with both preferences and. However, when the fraction of individuals always wearing a mask achieves a critical point, strengthening the filterability from outside to the face becomes more effective because of the emerging hidden reality that the infected individuals become too few to utilize the filterability from their face to outside fully. (shrink)

Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov chain, for the transmission dynamics of West Nile virus in birds is developed based on the assumptions of its analogous deterministic model. The branching process is applied to derive the extinction threshold for the stochastic model and conditions for disease extinction or persistence. The probability of disease extinction computed from the branching process (...) is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of both models are compared to ascertain the effect of demographic stochasticity on West Nile virus dynamics. Analytical and numerical results show differences in model predictions and asymptotic dynamics between stochastic and deterministic models that are crucial for the prevention of disease outbreaks. It is found that there is a high probability of disease extinction if the disease emerges from exposed mosquitoes unlike if it emerges from infectious mosquitoes and birds. Finite-time to disease extinction is estimated using sample paths and it is shown that the epidemic duration is shortest if the disease is introduced by exposed mosquitoes. (shrink)

In recent years, the world knew many challenges concerning the propagation of infectious diseases such as avian influenza, Ebola, SARS-CoV-2, etc. These epidemics caused a change in the healthy balance of humanity. Also, the epidemics disrupt the economies and social activities of countries around the world. Mathematical modeling is a vital means to represent and control the propagation of infectious diseases. In this paper, we consider a stochastic epidemic model with a Markov process and delay, which generalizes many (...) models existing in the literature. In addition, we show the stochastic threshold for the extinction of the disease. Furthermore, numerical examples are discussed to confirm the theoretical result. (shrink)

Atmospheric pollution is deteriorating, which has affected the evolution of respiratory disease for the exposed human worldwide. Thus, exploring the influence of air pollution on the evolution of disease transmission dynamics is a significant issue. In this article, a stochastic susceptible-infective epidemic model in a polluted atmospheric environment is investigated. The existence and uniqueness of the global positive solution are established. In virtue of the aggregation methods and Lyapunov function, the sufficient conditions of disease extinction, persistence, and existence (...) of the stationary distribution are established, respectively. TakingPM2.5concentration as the air pollutant index, numerical simulations are carried out to support these results. Our results indicated that the disease transmission dynamics are significantly associated with the environmental atmospheric pollution and fluctuation. (shrink)

We investigate the dynamics of a nonautonomous stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis. By constructing suitable stochastic Lyapunov functions and using Has’minskii theory, we prove that there exists at least one nontrivial positive periodic solution of the system. Moreover, the sufficient conditions for extinction of the disease are obtained by using the theory of nonautonomous stochastic differential equations. Finally, numerical simulations are utilized to illustrate our theoretical analysis.

To date, our knowledge of Rift Valley fever disease spread and maintenance is still limited, as flooding, humid weather and presence of biting insects such as mosquitoes, have not completely explained RVF outbreaks. We propose a model that includes livestock, mosquitoes and ticks compartments structured according to their questing and feeding behaviour in order to study the possible role of ticks on the dynamics of RVF. To quantify disease transmission at the initial stage of the epidemic, we derive (...) an explicit formula of the basic reproductive number, $$R_0$$ R 0. Using the concept of Metzler matrix, we state necessary conditions for global asymptotic stability of the disease-free equilibrium. Results suggest that although host-ticks interactions may serve as disease reservoirs or disease amplifiers, the Aedes reproductive number should be kept under unity if disease post-epizootics activities are to be controlled. Results of both local and global sensitivity analysis of selected model parameters indicate that $$R_0$$ R 0 is more sensitive to the ticks attachment and detachment rates, probability of transmission from ticks to host and from host to ticks, length of infection in livestock and ticks death rate. Furthermore, when comparing the mean value of $$R_0$$ R 0 with that from previous studies which did not include ticks we found that our $$R_0$$ R 0 is very much larger resulting in an increase in the exponential phase of an outbreak. These findings suggest that if ticks are capable of transmitting the virus, they may be contributing to disease outbreaks and endemicity. (shrink)

This paper describes a traditional SIR type epidemic model with saturated infection rate and treatment function. The dynamics of the model is studied from the point of view of stability and bifurcation. Basic reproduction number is obtained and it is shown that the model system may possess a backward bifurcation. The global asymptotic stability of the endemic equilibrium is studied with the help of a geometric approach. Optimal control problem is formulated and solved. Some numerical simulation (...) works are carried out to validate our analytical results. (shrink)

We study the different solution strategy for solving epidemic model in different imprecise environment, that is, a Susceptible-Infected-Susceptible model in imprecise environment. The imprecise parameter is also taken as fuzzy and interval environment. Three different solution procedures for solving governing fuzzy differential equation, that is, fuzzy differential inclusion method, extension principle method, and fuzzy derivative approaches, are considered. The interval differential equation is also solved. The numerical results are discussed for all approaches in different imprecise environment.

This article deals with optimal control applied to vaccination and treatment strategies for an SIRS epidemic model with logistic growth and delay. The delay is incorporated into the model in order to modeled the latent period or incubation period. The existence for the optimal control pair is also proved. Pontryagin’s maximum principle with delay is used to characterize these optimal controls. The optimality system is derived and then solved numerically using an algorithm based on the forward and (...) backward difference approximation. (shrink)

Financing guarantee is an important means and key link to solve the financing difficulties of small- and medium-size enterprises. However, while financial guarantees alleviate the financing difficulties of SMEs, the complex guarantee relationships also constitute a new channel for credit risk contagion in the financial guarantee network. In this paper, we construct a model of credit risk contagion process of guarantee network based on SEIR and analyse the equilibrium point and stability of the model. Then, we find the (...) threshold value of risk contagion and further simulate the SEIR model dynamically to analyse the influence of each parameter of the model. The results show that the risk of the financing guarantee network begins to be widely contagious only when risk contagion threshold is greater than 1, and the conversion rate of exposed enterprises, removal rate of infected enterprises, nodal enterprises degree, and risk contagion rate have significant effects on the changes of individual density of susceptible, exposed, infected, and recovered enterprises. Combining the above findings, it is of great theoretical and practical significance to propose relevant countermeasures for credit risk control of financial guarantee network. (shrink)

In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, bilinear incidence rate and pulse vaccination strategy. We have defined two positive numbers $$R_{0}$$ R 0 and $$R_{1}$$ R 1. It is proved that there exists an infection-free periodic solution which is globally attractive if $$R_{0} 1.$$ R 1 > 1. The important mathematical findings for the dynamical behaviour of the Chlamydia disease model are also numerically verified using MATLAB. Finally epidemiological (...) implications of our analytical findings are addressed critically. (shrink)

The combined effect of coercion (public and private pressure), self-interest (competitive advantage) and conviction (intrinsically motivated or genuine) explain why environmental issues have become a key priority for companies. While research has explored coercion and competitive advantage, the role of conviction has received little attention. This paper aims to address this gap. Conviction, which has been correlated with institutional and individual drivers, offers more stable results and a potential multiplier effect as good examples are disseminated by imitation throughout an industry. (...) While the role of imitation has drawn increasing attention of business management studies, it has received scant attention in research on sustainability. This is the second gap this paper aims to address, contributing to the literature on sustainability in two ways: firstly, we will further explore the role of conviction in environmental sustainability; secondly, employing a compartmental model of epidemic propagation, used for other social phenomena, we model the role genuine examples by leaders can play within an industry and the dissemination of good behavior by imitation. Defining genuine conviction as the voluntary mitigation of the externalities of a firm's operations beyond that required by law or the market, substantiated in the responsible behavior of its leaders, our model discovers patterns that policymakers could use to create a “sustainability epidemic”. We suggest mathematical models of epidemics can be applied to sustainability, offering a fresh perspective on the phenomenon of imitation, allowing us to discover how some cultural and social habits can be used. (shrink)

Let the individuals of a population be divided into two groups with different personal habits. The core group is associated with health risk behaviors; the non-core group avoids unhealthy activities. Assume that the infected individuals of the core group can spread a contagious disease to the whole population. Also, assume that cure does not confer immunity. Here, an epidemiological model written as a set of ordinary differential equations is proposed to investigate the infection propagation in this population. In the (...) model, migrations between these two groups are allowed; however, the transitions from the non-core group into the core group prevail. These migrations can be either spontaneous or stimulated by social pressure. It is analytically shown that, in the scenario of spontaneous migration, the disease is either naturally eradicated or chronically persists at a constant level. In the scenario of stimulated migration, in addition to eradication and constant persistence, self-sustained oscillations in the number of sick individuals can also be found. These analytical results are illustrated by numerical simulations and discussed from a public health perspective. (shrink)

In this article, we investigated a deterministic model of pneumonia-meningitis coinfection. Employing the Atangana–Baleanu fractional derivative operator in the Caputo framework, we analyze a seven-component approach based on ordinary differential equations. Furthermore, the invariant domain, disease-free as well as endemic equilibria, and the validity of the model’s potential results are all investigated. According to controller design evaluation and modelling, the modulation technique devised is effective in diminishing the proportion of incidences in various compartments. A fundamental reproducing value is (...) generated by exploiting the next generation matrix to assess the properties of the equilibrium. The system’s reliability is further evaluated. Sensitivity analysis is used to classify the impact of each component on the spread or prevention of illness. Using simulation studies, the impacts of providing therapy have been determined. Additionally, modelling the appropriate configuration demonstrated that lowering the fractional order from 1 necessitates a rapid initiation of the specified control technique at the largest intensity achievable and retaining it for the bulk of the pandemic’s duration. (shrink)

The aim of the present study was to investigate relationships among epidemic risk perception, perceived stress, mental health, future time perspective, and confidence in society during the novel coronavirus disease pandemic in China. Especially, we wonder that whether perceived stress mediates associations between epidemic risk perception and mental health and that whether future time perspective and confidence in society moderate the link between perceived stress and mental health. This cross-sectional study was conducted among 693 Chinese adults aged 18–60 (...) years. The results showed that epidemic risk perception was positively related to perceived stress, depression, and anxiety. The correlations between epidemic risk perception and depression and anxiety were reduced when perceived stress was included, suggesting that perceived stress mediated these relationships. Moreover, the boundary conditions for the associations among perceived stress, depression, and anxiety were found in the study. Specifically, positive future time perspective could buffer the negative effects of perceived stress on depression, and confidence in society could weaken the negative effects of perceived stress on anxiety. Based on these findings, practical guidance and theoretical implications are provided for the public to maintain mental health during COVID-19 pandemic. Limitations and future directions are also discussed. (shrink)

HIV-related state laws are being created transnationally though the use of omnibus model laws. In 2004, the US Agency for International Development funded the creation of one such guidance text known as the USAID/Action for West Africa Region Model Law, or N'Djamena Model Law, which led to the rapid spread of HIV/AIDS laws, including the criminalisation of HIV transmission, across much of West and Central Africa . In this article, I explicate how an epidemic of highly (...) problematic legislation spread across the region as a result of a text-mediated work process enabled through model laws. I theorise the textual genre of model laws arguing that these texts are best understood as ‘preoperative documents’ which, when activated, can lead to swift legislative reform in and beyond the field of HIV/AIDS governance. The legislative process being investigated was made visible through participant observation, archival research, textual analysis and informant interviews with national and international stakeholders . This involved ethnographic research in Canada, the USA, Switzerland, Austria, South Africa and Senegal . The untold policy processes and narratives explored in this article make evident how the work of contesting problematic HIV/AIDS model laws and newly drafted state laws involves both creating new texts and contesting the legitimacy and efficacy of others. (shrink)

BackgroundMore than 15% of Chinese respondents reported somatic symptoms in the last week of January 2020. Promoting resilience is a possible target in crisis intervention that can alleviate somatization.ObjectivesThis study aims to investigate the relationship between resilience and somatization, as well as the underlying possible mediating and moderating mechanism, in a large sample of Chinese participants receiving a crisis intervention during the coronavirus disease 2019 epidemic.MethodsParticipants were invited online to complete demographic information and questionnaires. The Symptom Checklist-90 somatization subscale, (...) 10-item Connor–Davidson resilience scale, and 10-item Perceived Stress Scale were measured.ResultsA total of 2,557 participants were included. Spearman correlation analysis revealed that lower resilience was associated with more somatic symptoms. The conditional process model was proved. The interaction effects between perceived stress and sex predicted somatization.ConclusionResilience is a key predictor of somatization. The mediating effects of perceived stress between resilience and somatization work in the context of sex difference. Sex-specific intervention by enhancing resilience is of implication for alleviating somatization during the coronavirus disease 2019 epidemic. (shrink)

Neospora caninum infection, one of the major causes of abortions in dairy cattle, has brought a huge loss to farmers worldwide. In this study, we develop a six-compartment susceptible-infected model of N. caninum transmission which is later reduced to a two-equation system. Potential controls including medication, test-and-cull, and vaccination are proposed and analyzed, and the corresponding reproduction numbers are derived. The conditions for the global stabilities of disease-free and endemic equilibria are investigated with analytical solutions and geometric approach. Furthermore, (...) uncertainty and sensitivity analysis shows that three control strategies are effective towards the varied environment, whereas the effectiveness of each measure highly depends on parameters related to control actions. Dynamics of reproduction numbers illustrate that disease elimination can be achieved by three types of controls: adopting medication with medicine efficacy higher than 0.4 to prevent vertical transmission, implementing test-and-cull with culling coverage larger than 0.3, and taking vaccine with coverage larger than 0.1. Numerical results suggest that preventive measures should at least include the prevention of access of other hosts, such as dogs, to cattle; otherwise, these control measures will lose effectiveness. Our presented study provides guidance for decision-making on N. caninum infected farm management. (shrink)

In the real world, individual resources are crucial for patients when epidemics outbreak. Thus, the coupled dynamics of resource diffusion and epidemic spreading have been widely investigated when the recovery of diseases significantly depends on the resources from neighbors in static social networks. However, the social relationships of individuals are time-varying, which affects such coupled dynamics. For that, we propose a coupled resource-epidemic dynamic model on a time-varying multiplex network to synchronously simulate the resource diffusion and (...) class='Hi'>epidemic spreading in dynamic social networks. The equilibrium analysis of the coupled model is conducted in a general scenario where the resource generation varies between susceptible and infected states and the recovery rate changes between resourceful and noresource states. By using the microscopic Markov chain approach and Monte Carlo simulations, we determine a probabilistic framework of the intralayer and interlayer dynamic processes of the coupled model and obtain the outbreak threshold of epidemic spreading. Meanwhile, the experimental results show the trivially asymmetric interactions between resource diffusion and epidemic spreading. They also indicate that the stronger activity heterogeneity and the larger contact capacity of individuals in the resource layer can more greatly promote resource diffusion, effectively suppressing epidemic spreading. However, these two individual characters in the epidemic layer can cause more resource depletion, which greatly promotes epidemic spreading. Furthermore, we also find that the contact capacity finitely impacts the coupled dynamics of resource diffusion and epidemic spreading. (shrink)

In this paper, we propose a nonlinear coupled model to study the two interacting processes of awareness diffusion and epidemic spreading on the same individual who is affected by different neighbor behavior status on multiplex networks. We achieve this topology scenario by two kinds of factors, one is the perception factor that can change interplay between different layers of networks and the other is the neighbors’ behavior status that can change the infection rate in each layer. According to (...) the microscopic Markov chain approach, we analyze the dynamical evolution of the system and derive the theoretical epidemic threshold on uncorrelated heterogeneous networks, and then, we validate the analysis by numerical simulation and discuss the final size of awareness diffusion and epidemic spreading on a scale-free network. With the outbreak of COVID-19, the spread of epidemic in China prompted drastic measures for transmission containment. We examine the effects of these interventions based on modeling of the awareness-epidemic and the COVID-19 epidemic case. The results further demonstrate that the epidemic spreading can be affected by the effective transmission rate of the awareness and neighbors’ behavior status. (shrink)

Studies have shown that as MRI T2 relaxation time lengthens there is a shift toward more unbound or “free-water” and less partitioning of the protein/lipid molecules per unit volume. A shift toward less water partitioning or lengthened MRI T2 relaxation time is linearly related to reduced high frequency EEG amplitude, reduced short distance EEG coherence, increased long distance EEG coherence, and reduced cognitive functioning (Thatcher et al. 1998a; 1998b).

Tuberculosis is caused by bacillus Mycobacterium tuberculosis. In this study, a mathematical model of tuberculosis is analyzed. The numerical behaviour of the considered model is analyzed including basic reproduction number and stability. We applied three numerical techniques to this model, i.e., nonstandard finite difference scheme, Runge–Kutta method of order 4, and forward Euler scheme. NSFD scheme preserves all the essential properties of the model. Acquired results corroborate that NSFD scheme converges for each step size. While the (...) other two schemes failed to preserve some properties of the model such as positivity and convergence. A graphical comparison presented in this study confirms the numerical stability of the NSFD technique shown here is maintained over a large area. (shrink)

The susceptible-transmissible-removed (STR) model is a deterministic compartment model, based on the susceptible-infected-removed (SIR) prototype. The STR replaces 2 SIR assumptions. SIR assumes that the emigration rate (due to death or recovery) is directly proportional to the infected compartment’s size. The STR replaces this assumption with the biologically appropriate assumption that the emigration rate is the same as the immigration rate one infected period ago. This results in a unique delay differential equation epidemic model with the (...) delay equal to the infected period. Hamer’s mass action law for epidemiology is modified to resemble its chemistry precursor—the law of mass action. Constructing the model for an isolated population that exists on a surface bounded by the extent of the population’s movements permits compartment density to replace compartment size. The STR reduces to a SIR model in a timescale that negates the delay—the transmissible timescale. This establishes that the SIR model applies to an isolated population in the disease’s transmissible timescale. Cyclical social interactions will define a rhythmic timescale. It is demonstrated that the geometric mean maps transmissible timescale properties to their rhythmic timescale equivalents. This mapping defines the hybrid incidence (HI). The model validation demonstrates that the HI-STR can be constructed directly from the disease’s transmission dynamics. The basic reproduction number (R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}) is an epidemic impact property. The HI-STR model predicts that R0∝ρnB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0 \propto \root \mathfrak{B} \of {\rho_n}$$\end{document} where ρn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document} is the population density, and B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{B}}$$\end{document} is the ratio of time increments in the transmissible- and rhythmic timescales. The model is validated by experimentally verifying the relationship. R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}’s dependence on ρn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document} is demonstrated for droplet-spread SARS in Asian cities, aerosol-spread measles in Europe and non-airborne Ebola in Africa. (shrink)

Various forms of research are essential in emergency, disaster and disease outbreak situations, but challenges exist including the long length of time it takes to get research proposals approved. Consequently, it would be very advantageous to have an acceptable model for efficient coordination and communication between and among research ethics committees/IRBs and ministries of health, and templates for expediting ethical review of research proposals in emergency and epidemic situations to be used across the Caribbean and in other low (...) and middle income countries. This project involved a literature search and the interviewing of ministry of health officials, public health practitioners, and research ethics committee/IRB members in Jamaica and St. Lucia, to obtain suggestions for the best model for efficient coordination and communication between research ethics committees, and developed a template for expediting review of research protocols in epidemic and emergency conditions. (shrink)

Quantitative assessments of when infectious disease outbreaks end are crucial, as resources targeted towards outbreak responses typically remain in place until outbreaks are declared over. Recent improvements and innovations in mathematical approaches for determining when outbreaks end provide public health authorities with more confidence when making end-of-outbreak declarations. Although quantitative analyses of outbreaks have a long history, more complex mathematical and statistical methodologies for analysing outbreak data were developed early in the 20th century and continue to be refined. Historically, such (...) methodologies focused primarily on factors affecting the early and middle phases of an outbreak, with less attention given to determining how and when outbreaks end. This review discusses mathematical modelling methods from the last 20 years that have been developed for determining the ends of infectious disease outbreaks, and considers factors that affect the accuracy of such determinations. When disease surveillance systems provide timely and representative data to inform models, the timings of end-of-outbreak declarations can be fine-tuned to allow outbreaks to be declared over quickly and with a low risk of being incorrect. Premature declarations that outbreaks are over can undermine earlier achievements in disease control and may result in a resurgence of cases, but unnecessary delays in declaring outbreaks over can cause significant economic and social harm. Appropriate declarations that balance the benefits of relaxing control measures against the risk of a surge in cases allow public health resources to be conserved (and economic and social pressures to be reduced) while limiting the potential for additional transmission. (shrink)

As COVID-19 drags on and new vaccines promise widespread immunity, the world's attention has turned to predicting how the present pandemic will end. How do societies know when an epidemic is over and normal life can resume? What criteria and markers indicate such an end? Who has the insight, authority, and credibility to decipher these signs? Detailed research on past epidemics has demonstrated that they do not end suddenly; indeed, only rarely do the diseases in question actually end. This (...) article examines the ways in which scholars have identified and described the end stages of previous epidemics, pointing out that significantly less attention has been paid to these periods than to origins and climaxes. Analysis of the ends of epidemics illustrates that epidemics are as much social, political, and economic events as they are biological; the “end,” therefore, is as much a process of social and political negotiation as it is biomedical. Equally important, epidemics end at different times for different groups, both within one society and across regions. Multidisciplinary research into how epidemics end reveals how the end of an epidemic shifts according to perspective, whether temporal, geographic, or methodological. A multidisciplinary analysis of how epidemics end suggests that epidemics should therefore be framed not as linear narratives—from outbreak to intervention to termination—but within cycles of disease and with a multiplicity of endings. (shrink)

We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue (...) $$\mathcal{R}_\sigma$$ of the basic reproduction number $$\mathcal{R}_0$$ of the underlying deterministic model, with $$\mathcal{R}_\sigma \le \mathcal{R}_0$$. We prove that the disease-free equilibrium is almost sure exponentially stable if $$\mathcal{R}_\sigma <1$$. (shrink)

In this paper, we present and defend the theoretical framework of an empirical model to describe people’s fundamental moral attitudes (FMAs) to animals, the stratification of FMAs in society and the role of FMAs in judgment on the culling of healthy animals in an animal disease epidemic. We used philosophical animal ethics theories to understand the moral basis of FMA convictions. Moreover, these theories provide us with a moral language for communication between animal ethics, FMAs, and public debates. (...) We defend that FMA is a two-layered concept. The first layer consists of deeply felt convictions about animals. The second layer consists of convictions derived from the first layer to serve as arguments in a debate on animal issues. In a debate, the latter convictions are variable, depending on the animal issue in a specific context, time, and place. This variability facilitates finding common ground in an animal issue between actors with opposing convictions. (shrink)

The globalization in business and tourism becomes crucial more and more for the economical sustainability of local communities. In the presence of an epidemic outbreak, there must be such a decision on the policy by the host community as whether to accept visitors or not, the number of acceptable visitors, or the condition for acceptable visitors. Making use of an SIRI type of mathematical model, we consider the influence of visitors on the spread of a reinfectious disease in (...) a community, especially assuming that a certain proportion of accepted visitors are immune. The reinfectivity of disease here means that the immunity gained by either vaccination or recovery is imperfect. With the mathematical results obtained by our analysis on the model for such an epidemic dynamics of resident and visitor populations, we find that the acceptance of visitors could have a significant influence on the disease’s endemicity in the community, either suppressive or supportive. (shrink)

The current major models of coexistence of species on the same resources are briefly summarized. It is then shown that analysis of supposedly competitive systems in terms of the physical four dimensions of phase-space is sufficient to understand the causes for coexistence and for competitive exclusion. Thus, the multiple dimensions of niche theory are reduced to factors which define the magnitudes of the phase-spatial system, in particular the boundaries of population spaces and of periods of activity. Excluding possible cooperative interaction (...) between consumers, it appears that coexistence of species on thesame kind of limiting resource is possible only in cases of compartmentalization either in space, or in time, of resource consumption, i.e. if each consumer species disposes of a separate resource supply. Three criteria were found to be decisive for successful compartmentalization (i.e. for coexistence): 1. the vector of the resource flow; 2. relative mobility between consumers and resource units; 3. dependence or independence of resource flow on previous consumption. The traditional terminology of niche theory and of competition theory in general proved to be inadequate for analytical treatment of problems of coexistence. (shrink)

Pre-existing medical conditions and co-infections are common to all human populations, although the natures of the pre-existing conditions and the types of co-infections vary. For these reasons, among others, the arrival of a highly infectious pathogenic agent may differentially affect the disease burden in different sub-populations, as a function of varying combinations of endemic disease, chronic disease, genetic or epigenetic vulnerabilities, compromised immunological status, and socially determined risk exposure. The disease burden may also vary considerably by age cohort and socio-economic (...) status. The social consequences of infection, the medical sequelae, and the paths of recovery from infection may also vary, according to these variables. As a result, different sub-populations may have different experiences of a disease process, including when and how an epidemic comes to an end. This essay suggests that historians' engagement with path-breaking biological and medical anthropological research will allow new approaches to understanding disease processes that will enrich the study of epidemics and their endings. It is organized in three sections. The first discusses some general approaches to and assumptions about epidemics that are used by many historians. The second introduces new perspectives on the study of historical epidemics opened up by the medical anthropological concept of syndemic disease interactions and by an engagement with biological scientific perspectives. It briefly discusses two rural epidemics-one of anemia caused by the syndemic interaction of hookworm and malaria co-infections in early 20th-century British Malaya, and the other of rebound infections caused by the loss of acquired immunity to falciparum malaria in mid-20th-century Liberia-that illustrate, respectively, the utility of the concept of syndemic disease interactions and the centrality of immunological status in understanding epidemic outbreaks in these discrete populations. The third section addresses some of the research considerations involved in moving beyond the single pathogen model of epidemic disease. (shrink)

In order to explore, from the perspective of the social ecological model, the relationship and its mechanism linking public risk familiarity and mental health during the new coronary pneumonia epidemic, the new coronary pneumonia epidemic risk perception scale, psychological resilience scale, Chinese mental health scale, and SARS familiarity scale were used 741 members of the public were surveyed as research objects. The results show that: When gender, age, and educational background are controlled, risk familiarity has a significant (...) positive predictive effect on public mental health; Risk familiarity predicts mental health through the mediating effect of mental toughness; The mediating effect of mental toughness is moderated by the public’s familiarity with SARS. Specifically, for members of the public with low SARS familiarity, the indirect effect of risk familiarity on mental health through mental toughness is smaller than that for those with high SARS familiarity. The results of this study integrate psychological resilience into the theory of risk cognition, which has implications for the improvement of public mental health. (shrink)

Over the last few decades, the Internet has brought about a myriad of benefits to almost every aspect of our daily lives. However, malware attacks have also widely proliferated, mainly aiming at legitimate network users, resulting in millions of dollars in damages if proper protection and response measures are not settled and enforced. In this context, the paper at hand proposes MalSEIRS, a novel dynamic model, to predict malware distribution in a network based on the SEIRS epidemiological model. (...) As a result, the time-dependent rates of infection, recovery, and loss of immunity enable us to capture the complex dynamism of malware spreading behavior, which is influenced by a variety of external circumstances. In addition, we describe both offensive and defensive techniques, based on the proposed MalSEIRS model, through extensive experimentation, as well as disclosing real-life malware campaigns that can be better understood by using the suggested model. (shrink)

Although every emerging infectious disease occurs in a unique context, the behaviour of previous pandemics offers an insight into the medium- and long-term outcomes of the current threat. Where an informative historical analogue exists, epidemiologists and policymakers should consider how the insights of the past can inform current forecasts and responses.

Since the sudden outbreak of the coronavirus disease 2019 epidemic in 2020, the second language learning patterns of students in mainland China have encountered new challenges that have had a psychological impact on mainland Chinese students. The epidemic has not only inconvenienced students’ normal second language learning but also greatly affected the second language learning patterns of mainland Chinese students. In the post-epidemic era, more and more students are becoming accustomed to studying and learning a second language (...) online. The level of informatization of second language learning patterns of students in mainland China has increased significantly. This study first analyses the mechanisms of change in second language learning patterns and further analyses the influence of knowledge background on the perception of second language learning patterns on this basis. To design the influencing factors of second language learning patterns, a questionnaire was used to investigate the influence of knowledge background on the perception of second language learning patterns. The survey was conducted on students who were learning a second language in mainland China. Then, the survey data were statistically analyzed. In analyzing the influence of effect on second language learning behaviors of students in mainland China, observed variables were designed, including observed variables of affective factors and learning behaviors. After that, the findings of the experiment were summarized based on the results of the questionnaire survey, and the positive influence of emotional factors on second language learning behaviors of mainland Chinese students in the post-development era was concluded. (shrink)

Previous studies revealed that the susceptibility, contacting preference, and recovery probability markedly alter the epidemic outbreak size and threshold. The recovery probability of an infected node is closely related to its obtained resources. How to allocate limited resources to infected neighbors is extremely important for containing the epidemic spreading on complex networks. In this paper, we proposed an epidemic spreading model on complex networks, in which we assume that the node has heterogeneous susceptibility and contacting preference, (...) and susceptible nodes are willing to share their resources to neighbors. Through a developed heterogeneous mean-field theory and a large number of numerical simulations, we find that the recovered nodes provide resources uniformly to their infected neighbor nodes, and the epidemic spreading can be suppressed optimally on homogeneous and heterogeneous networks. Besides, altering the susceptibility and contacting preference does not qualitatively change the results. The susceptibility of the node decreases, which makes the outbreak threshold of epidemic spreading increase, and the outbreak size decreases. Our theory agrees well with the numerical simulations. (shrink)

Kendall's (1956) approach to the general epidemic is generalized by dropping the assumptions of constant infectivity and random recovery or death of ill individuals. A great deal of attention is paid to the biological background and the heuristics of the model formulation. Some new results are: (l) the derivation of Kermack's and McKendrick's integral equation from what seems to be the most general set of assumptions in section 2.2, (2) the use of Kermack's and McKendrick's final value equation (...) to arrive at a finite time version of the threshold theorem for the general case, comparable to that for the case of only one Markovian state of illness in section 2.5, (3) the analysis of the behaviour of the solutions of the integral equation when the starting infection approaches zero in section 2.7, (4) the derivation of the probability structure of a general branching process, after conditioning on extinction in section 3.6, (5) the statement of the generalized versions of Kendall's ideas in the form of precise limit conjectures in section 4, (6) the derivation of a closed expression for the limit epidemic resulting from (3) in appendix 4. (shrink)

COVID-19 epidemic models raise important questions for science and philosophy of science. Here I provide a brief preliminary exploration of three: what kinds of predictions do epidemic models make, are they causal models, and how do different kinds of epidemic models differ in terms of what they represent?