A restricted epidemic SIR model with elementary solutions

Abstract

The mathematical epidemic SIR (Susceptible–Infected–Recovered) model is targeted to obtain full elementary solutions under restrictive assumptions in this paper. To achieve the aim, the traditional SIR model is modified in such a manner that the interaction between the susceptible and infected leading to new infected person takes place proportional to the susceptible square root and infected compartments, in place of the product of susceptible and infected class as in the classical model. First, equilibrium points of the new model are identified and their stability analysis is examined. Such a variant of the SIR model enables us to define a basic reproduction number in terms of the ratio of squares of infection and recovery rates. Elementary solutions of the model are next formed based on the simple hyperbolic functions. Solutions of this form are shown to be valid for a confined interval of basic reproduction number. Graphical illustrations are finally given for some selected epidemic parameters. The present analytical solutions can be used to test the accuracy of a number of numerical simulation methods being developed for various other SIR models recently being investigated.