Model analysis for an HIV infectious disease using elasticity and sensitivity techniques

Abstract

<p>The human immunodeficiency virus (HIV) is an infection that mainly impacts CD4⁺ T cells inside the immune system, causing a gradual decline in immunological function. If untreated, this can lead to acquired immunodeficiency syndrome (AIDS), a disorder in which the body becomes extremely susceptible to opportunistic infections due to a severely compromised immune system. This paper presents a rigorous analysis of a mathematical model that describes the dynamics of HIV infectious disease transmission. There are some key outputs of the study presented. First, we derive the basic reproduction number (<italic>R</italic>₀) which determines the threshold for disease persistence. Then, we analyze the stability of the disease-free and endemic equilibria. After that, we perform a sensitivity analysis to identify the key parameters that influence the dynamics of the system. The basic reproduction number (<italic>R</italic>₀) is calculated using the next generation matrix approach. The stability of the disease-free and endemic equilibria is investigated to understand the long-term behavior of the model. A sensitivity analysis is conducted to determine which model parameters have the greatest impact on the spread of HIV. The model includes a class of nonlinear ordinary differential equations, and has both infection-free and endemic infection equilibrium points. The elasticity of <italic>R</italic>₀ related to the model parameters is determined, and the local sensitivities between the model variables and parameters are numerically evaluated using non-normalization, half-normalization, and full-normalization techniques. The numerical results show that there are different sensitivities between model compartments and model parameters. The findings offer valuable insights for designing effective control strategies and optimizing interventions aimed at curbing the spread of HIV.</p>