Dynamics of interacting SIRS+V models of infectious disease spread

The purpose of this work is study of processes of spread of infectious diseases in metapopulations interacted through spontaneous migration. The method is based on theoretical examination of the structure of the phase space of a system of coupled ODEs and numerical study of the transient processes in dependence on the coupling between subsystems. Results. A model of interacting populations in the form of two identical SIRS+V systems with mutual diffusion coupling is proposed and investigated. It was found that the long-term dynamics of the metapopulation does not differ from the behavior of an individual population; however, its transitional dynamics may be different and significantly depends on the values of the migration coefficients of infected and healthy individuals. In particular, under certain conditions, a complete suppression of infection waves can be observed in a secondarily infected population. Discussion. Despite the extreme simplicity of the model and the observed regimes, the results may be interesting from the point of view of practical recommendations for planning a strategy to combat transmission between communities, since they reveal the influence of the intensity of migrations of sick and healthy individuals on the spread of the epidemic in metapopulations.