Application of an age-structured deterministic endemic model for disease control in Nigeria

Abstract

This paper focuses on the development and analysis of the endemic model for disease control in an aged-structured population in Nigeria. Upon the model framework development, the model equations 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 susceptible-exposed-infected-removed-undetectable=untransmissible-susceptible (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 0≤R_0<1. 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.