In this paper, we present a deterministic model for the population dynamics of HIV/AIDS, wherein some individuals at the severe symptomatic phase of HIV develop serious opportunistic infections (OIs) such cryptococcal, tuberculous, pneumococcal, and other bacterial meningitis due to an inappropriate treatment or lack of counseling. OIs are responsible for significant mortality and disability on individuals with HIV in many countries. Cryptococcal meningitis (CM) is among frequent OIs responsible for significant mortality and disability of individuals with HIV in limited resource settings. However, there are also cases of high mortality due to CM on HIV-uninfected individuals, but the burden of CM is more frequent in people living with HIV. We proved the global stability of the disease-free as well as the endemic equilibrium points. In addition, we performed the study of sensitivity analysis of the basic reproduction number with the parameters of the model as well as with some compartmental classes. We illustrated our theoretical results by way of numerical simulations using a projection on the HIV historical data of South Africa since 2024. Our analysis showed that a combination of ART and OI specific treatments may reduce the number of death related cases.
Citation: Mozart Umba Nsuami, Peter Joseph Witbooi. Modeling the population dynamics of HIV/AIDS with opportunistic infections at the severe stage of HIV[J]. Mathematical Biosciences and Engineering, 2025, 22(9): 2249-2268. doi: 10.3934/mbe.2025082
In this paper, we present a deterministic model for the population dynamics of HIV/AIDS, wherein some individuals at the severe symptomatic phase of HIV develop serious opportunistic infections (OIs) such cryptococcal, tuberculous, pneumococcal, and other bacterial meningitis due to an inappropriate treatment or lack of counseling. OIs are responsible for significant mortality and disability on individuals with HIV in many countries. Cryptococcal meningitis (CM) is among frequent OIs responsible for significant mortality and disability of individuals with HIV in limited resource settings. However, there are also cases of high mortality due to CM on HIV-uninfected individuals, but the burden of CM is more frequent in people living with HIV. We proved the global stability of the disease-free as well as the endemic equilibrium points. In addition, we performed the study of sensitivity analysis of the basic reproduction number with the parameters of the model as well as with some compartmental classes. We illustrated our theoretical results by way of numerical simulations using a projection on the HIV historical data of South Africa since 2024. Our analysis showed that a combination of ART and OI specific treatments may reduce the number of death related cases.
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Mozart Umba Nsuami, Peter Joseph Witbooi. Modeling the population dynamics of HIV/AIDS with opportunistic infections at the severe stage of HIV[J]. Mathematical Biosciences and Engineering, 2025, 22(9): 2249-2268. doi: 10.3934/mbe.2025082
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