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APPLICATION OF AN AGE-STRUCTURED DETERMINISTIC ENDEMIC MODEL FOR DISEASE CONTROL IN NIGERIA (Research Paper Sample)

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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 the 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 (SERIUS) 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.

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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 R0=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≤R0<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.
Keyword: Susceptible, Exposed, Latent, Infectious, Removed, Recovery, Undetectable.
1 INTRODUCTION
The estimation of the rate of prevalence of HIV/AIDS in Nigeria is very key for the administration of relevant interventions by relevant stakeholders in the health sector and the Nigerian Center for Disease Control (NCDC) hence in this paper we develop and evaluate the new deterministic endemic age-structured SEIRUS compartmental model of the HIV/AIDS dynamics in Nigeria and a two-age-structured population framework for a deterministic endemic model is constructed for the development of an endemic deterministic model with Undetectable=Untrasmitable viral load compartment.
In recent study by [1] and an earliest study by [2] among others have been very motivational for this study and were focused on the epidemiology of HIV/AIDS using various models like SIR, SEIR, SIRS, SICA models formulated for epidemic case of disease control. However, because these earliest models did not take into account the endemicity of the diseases, this study therefore focuses on the endemic nature, developing and evaluating a deterministic endemic model for the control of further spread and eventual eradication of the disease in Nigeria.
2 THE MODEL VARIABLES AND PARAMETERS

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