Existence of epidemic waves in a disease transmission model with two-habitat population

A three variable mathematical model describing the propagation of an infectious disease in a human population is proposed and analyzed. The human population is assumed to live in two distinct habitats with no inter-habitat migration. The infectious agent disperse randomly among the said habitats. Methods of upper and lower solutions are used to establish the existence of traveling wave solutions connecting the trivial with the nontrivial equilibrium. The critical wave speed required for the existence of such wave solutions has been found out and shown to depend on different system parameters together with the dispersal rate.

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