On the integrability of the SIRD epidemic model

Abstract

In this paper, Lie symmetry and Painleve Techniques are applied to the SIRD (Susceptible, Infected, Recovered and Dead) model. A demonstration of the integrability of the model is provided to present an explicit solution. The study revealed a complex chaotic behaviour at a specific value of constant constraints. However, the system fails to pass the Painleve test while constraints reach values equivalent to the corresponding complex chaotic behaviour. The two-dimensional Lie symmetry algebra and the commutator table of the infinitesimal generators are obtained. Lie symmetry analysis serves to linearize the nonlinear system and find the corresponding exact solution.