Disease control in an age-structured population in south Africa using the susceptible-exposed-infected-removed-undetectable-susceptible (SEIRUS) model

Abstract

South Africa being the country in the world to with the highest rate of prevalence of HIV/AIDS with over 7million cases calls for a dare need to analyze and implement strategies to combat the further spread of the virus. In this study the SEIRUS model was analyzed for disease control in an aged-structured population in the country. The model equations for ordinary differential equation of the model were transformed into proportions with rate of change of the different compartments forming the model, thereby reducing the model equations from twelve to ten homogenous ordinary differential equations. The model exhibits two equilibria, the endemic state and the disease-free equilibrium state while successfully achieving a Reproductive Number R_0=0. The deterministic endemic SEIRUS model is analyzed for the existence and stability of the disease-free equilibrium state. We established that a disease-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number R_0=0. Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect treatment rate and the net transmission rate on recovery for both juvenile and adult sub-population in an age-structured population.