On the Generalization of the Standard SIR Model of Infectious Diseases and its HAM Solution

In this paper, a general model system of equations for the standard SIR epidemic models for simulating the spread of infectious diseases is formulated and its solution is determined using the Homotopy Analysis Method (HAM). The system fits all autonomous SIR epidemic models involving the three classes, susceptibles (S(t)), infectious (I(t)), and the recovered/removed (R(t)). Illustrative examples are then used to verify the validity of the analytical solution, and further compared with the classical fourth-order Runge-Kutta schemes, which reveals the power of the HAM as a tool for solving nonlinear systems of ODEs.