Transmission Dynamics of a Two-City SIR Epidemic Model with Transport-Related Infections

Abstract

A two-city SIR epidemic model with transport-related infections is proposed. Some good analytical results are given for this model. If the basic reproduction number ${\Re }_{0\gamma }\le 1$, there exists a disease-free equilibrium which is globally asymptotically stable. There exists an endemic equilibrium which is locally asymptotically stable if the basic reproduction number ${\Re }_{0\gamma }>1$. We also show the permanence of this SIR model. In addition, sufficient conditions are established for global asymptotic stability of the endemic equilibrium.