Dispersal engendered synchronization and stability of mediated infectious diseases in the patchy environment using mean-field diffusive coupling

Mobility of humans and mediating agents significantly affects the scope of mediated infectious diseases. The spatial transmission of mediated infectious diseases ultimately depends on the movement of hosts and mediators. To comprehend the causes, predict, evaluate, and restrict epidemic transmission, it is crucial to investigate the dynamics of mediated infectious diseases in the presence of mobility. The network of mediators and the host metapopulation are related to the spatial coupling for disease dissemination. Thus, in this article, the metapopulation dynamics of the mediated infectious disease model is studied in a patchy environment where the hosts and mediators population is divided into sub-population. Two networks are used to represent the patchy environment: the hosts or humans network and the mediators network. Mean field diffusive coupling is used to connect the network patches. Both homogeneous and heterogeneous networks are investigated in terms of dynamics. Dispersal engenders the patches of corresponding networks to synchronize and reach bistable states of non-trivial amplitude death. Numerical simulations are performed to demonstrate the change from one state to another state, caused by transcritical bifurcation. The stability of disease free equilibrium and endemic equilibrium is also determined by the reproduction number R0.