Non-standard numerical method for a mathematical model of RSV epidemiological transmission

Respiratory Syncytial Virus (RSV) has long been recognized as the single most important virus causing acute severe respiratory-tract infections with symptoms ranging from rhinitis to bronchitis in children who may require hospitalization. Outbreaks of RSV occur every year and all children become infected within the first two years of life, and that overloads hospital casualty services. The transmission dynamics of RSV are strongly seasonal. Epidemics occur each winter in temperate climates and often coincide with the seasonal rainfall in tropical climates.In this paper we develop a non-standard numerical scheme for a SIRS seasonal epidemiological model for RSV transmission. This non-standard numerical scheme preserves the positivity of the continuous model and is applied to approximate the solution using different sizes of step.Finally this method is compared with some well-known explicit methods and simulations with data from Gambia and Finland are carried out.