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In this paper, we extend Liao’s newly invented MDDiM for a differential equation to a coupled system of nonlinear differential equations arising in SIR and SIS epidemic models. The method is novel, extended and is applied to the epidemiology models for the first time. Our analytical results agree well with the numerical results obtained by Runge-Kutta method. Errors ranging from 10−5 to 10−17 are obtained for a relatively few terms. Also, MDDiM uses less CPU time. Further, we present error plots and solution curves with numerical results to validate our approximate series solutions. This analytic approach is more general and can be used to analyze complicated models arising in mathematical biology, physics and engineering.

A Method of Directly Defining the inverse Mapping (MDDiM) for solutions of non-linear coupled systems arising in SIR and SIS epidemic models