Verma Tina, Gupta Arvind Kumar
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, 140001, Punjab, India.
Commun Nonlinear Sci Numer Simul. 2021 Nov;102:105927. doi: 10.1016/j.cnsns.2021.105927. Epub 2021 Jun 15.
Connectivity and rates of movement have profound effect on the persistence and extinction of infectious diseases. The emerging disease spread rapidly, due to the movement of infectious persons to some other regions, which has been witnessed in case of novel coronavirus disease 2019 (COVID-19). So, the networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. Motivated by the recent empirical evidence on the dispersal of infected individuals among the patches, we present the epidemic model SEIR (Susceptible-Exposed-Infected-Recovered) in which the population is divided into patches which form a network and the patches are connected through mean-field diffusive coupling. The corresponding unstable epidemiology classes will be synchronized and achieve stable state when the patches are coupled. Apart from synchronization and stability, the coupled model enables a range of rhythmic processes such as birhythmicity and rhythmogenesis which have not been investigated in epidemiology. The stability of Disease Free Equilibrium (or Endemic Equilibrium) is attained through cessation of oscillation mechanism namely Oscillation Death (OD) and Amplitude Death (AD). Corresponding to identical and non-identical epidemiology classes of patches, the different steady states are obtained and its transition is taking place through Hopf and transcritical bifurcation.
连通性和移动速率对传染病的持续存在和消亡有着深远影响。由于感染者向其他地区的移动，新兴疾病传播迅速，2019年新型冠状病毒病（COVID-19）就是如此。因此，直接传播的传染病的网络与流行病学在根本上是相互关联的。基于近期关于感染个体在斑块间扩散的实证证据，我们提出了易感-暴露-感染-康复（SEIR）流行病模型，其中种群被划分为形成网络的斑块，且斑块通过平均场扩散耦合相连。当斑块耦合时，相应的不稳定流行病学类别将实现同步并达到稳定状态。除了同步和稳定性外，耦合模型还能实现一系列节律过程，如双节律性和节律发生，这些在流行病学中尚未得到研究。通过振荡停止机制，即振荡死亡（OD）和振幅死亡（AD），实现无病平衡点（或地方病平衡点）的稳定性。对应于斑块相同和不同的流行病学类别，可得到不同的稳态，且其转变通过霍普夫分岔和跨临界分岔发生。
