Basic reproduction number of a multi-patch SVI model represented as a star graph topology

A mathematical model of Susceptible-Vaccinated-Infected (SVI) disease multi-patch model will be introduced in this article. Interaction between cities which are represented as a star graph involved in the model along with vaccination and medical treatment intervention. Human mobility is assumed to be constant between satellite patch and center patch. Basic reproduction number as the endemic indicator is constructed using a graph-theoretical approach. We find that basic reproduction number of the model is given by the reciprocal of the smallest positive root of a two degree polynomial. This method can be an alternative to determine a form of basic reproduction number for a complex system of ODE model.