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Communities are commonly not isolated but interact asymmetrically with each other, allowing the propagation of infectious diseases within the same community and between different communities. To reveal the impact of asymmetrical interactions and contact heterogeneity on disease transmission, we formulate a two-community SIR epidemic model, in which each community has its contact structure while communication between communities occurs through temporary commuters. We derive an explicit formula for the basic reproduction number R 0 , give an implicit equation for the final epidemic size z, and analyze the relationship between them. Unlike the typical positive correlation between R 0 and z in the classic SIR model, we find a negatively correlated relationship between counterparts of our model deviating from homogeneous populations. Moreover, we investigate the impact of asymmetric coupling mechanisms on R 0 . The results suggest that, in scenarios with restricted movement of susceptible individuals within a community, R 0 does not follow a simple monotonous relationship, indicating that an unbending decrease in the movement of susceptible individuals may increase R 0 . We further demonstrate that network contacts within communities have a greater effect on R 0 than casual contacts between communities. Finally, we develop an epidemic model without restriction on the movement of susceptible individuals, and the numerical simulations suggest that the increase in human flow between communities leads to a larger R 0 ., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

In this paper, we propose and study network epidemic models with demographics for disease transmission. We obtain the formula of the basic reproduction number R0 of infection for an SIS model with births or recruitment and death rate. We prove that if R0 ≤ 1 , infection-free equilibrium of SIS model is globally asymptotically stable; if R0 > 1 , there exists a unique endemic equilibrium which is globally asymptotically stable. It is also found that demographics has great effect on basic reproduction number R0. Furthermore, the degree distribution of population varies with time before it reaches the stationary state.

Consider the heterogeneity (e.g., heterogeneous social behaviour, heterogeneity due to different geography, contrasting contact patterns and different numbers of sexual partners etc.) of host population, in this paper, the authors propose an infection age multi-group SEIR epidemic model. The model system also incorporates the feedback variables, where the infectivity of infected individuals may depend on the infection age. In the direction of mathematical analysis of model, the basic reproduction number R0 has been computed. The global stability of disease-free equilibrium and endemic equilibrium have been established in the term of R0. More precisely, for R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable and for R0 > 1, they establish global stability of endemic equilibrium using some graph theoretic techniques to Lyapunov function method. By considering a numerical example, they investigate the effects of infection age and feedback on the prevalence of the disease. Their result shows that feedback parameters have different and even opposite effects on different groups. However, by choosing an appropriate value of feedback parameters, the disease could be eradicated or maintained at endemic level. Besides, the infection age of infected individuals may also change the behaviour of the disease, global stable to damped oscillations or damped oscillations to global stable. [ABSTRACT FROM AUTHOR]

Abstract: Outbreaks of infectious diseases may awaken the awareness of individuals, consequently, they may adjust their contact patterns according to the perceived risk from disease. In this paper, we assume that individuals make decisions on breaking or recovering links according to the information of diseases spreading which they have acquired. They will reduce some links when diseases are prevalent and have high risks; otherwise, they will recover some original links when the diseases are controlled or present minimal risk. Under such an assumption, we study the effects of information of diseases on the contact patterns within the population and on the dynamics of epidemics. By extensive simulations and theoretical analysis, we find that, due to the time-delayed information of diseases, both the density of the disease and the topology of the network vary with time in a periodic form. Our results indicate that the quality of information available to individuals can have an important effect on the spreading of infectious diseases and implications for related problems. [Copyright &y& Elsevier]