Abstract:
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 meanfield 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.
