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We present a compartmental SIR (susceptible–infected–recovered) model to describe the propagation of an infectious disease in a human population, when individuals travel between p different cities. The time needed for travel between any two locations is incorporated, and we assume that disease progression is possible during travel. The model is equivalent to an autonomous system of differential equations with multiple delays, and each delayed term is defined through a system of ordinary differential equations. We establish some necessary and sufficient conditions for the disease-free equilibrium of the model to be asymptotically stable.

Stability criteria for a multi-city epidemic model with travel delays and infection during travel