Abstract
This paper examines a mathematical modelling of HIV/AIDS transmission dynamics with drug resistance compartment. A nonlinear deterministic mathematical model for the problem is proposed using a system of ordinary differential equations. The aim of this study is to investigate the role of passive immunity and drug therapy in reducing the viral replication and transmission of the disease. The well possedness of the formulated model equations was proved and the equilibrium points of the model have been identified. In addition, the basic reproductive number that governs the disease transmission is obtained from the largest eigenvalue of the next-generation matrix. Both local and global stability of the disease free equilibrium and endemic of the model was established using basic reproduction number. The results show that the disease free equilibrium is locally asymptotically stable if the basic reproduction number is less than unity and unstable if the basic reproduction number is greater than unity. It is observed that if the basic reproduction is less than one then the solution converges to the disease free steady state i.e., disease will wipe out and thus the drug therapy is said to be successful. On the other hand, if the basic reproduction number is greater than one then the solution converges to endemic equilibrium point and thus the infectious cells continue to replicate i.e., disease will persist and thus the drug therapy is said to be unsuccessful. Sensitivity analysis of the model is performed on the key parameters to determine their relative importance and potential impact on the transmission dynamics of HIV/AIDS. Numerical results of the model show that a combination of passive immunity and drug therapy is the best strategy to reduce the disease from the community.
Highlights
Human Immunodeficiency Virus (HIV) is the causative agent of Acquired Immunodeficiency Syndrome (AIDS)
Okosun [7] presented the impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives on the transmission dynamics of the disease in a homogeneous population with constant immigration of susceptibles incorporating use of condom, screening of unaware infectives and treatment of the infected
The author [10] develop a mathematical model for HIV/AIDS transmission has been proposed, along with a control problem in which the objective was to determine the pre-exposure prophylaxis (PrEP) strategy that minimizes the number of individuals with pre-AIDS HIV infection, balanced against the costs associated with PrEP
Summary
Human Immunodeficiency Virus (HIV) is the causative agent of Acquired Immunodeficiency Syndrome (AIDS). Okosun [7] presented the impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives on the transmission dynamics of the disease in a homogeneous population with constant immigration of susceptibles incorporating use of condom, screening of unaware infectives and treatment of the infected. The author [10] develop a mathematical model for HIV/AIDS transmission has been proposed, along with a control problem in which the objective was to determine the pre-exposure prophylaxis (PrEP) strategy that minimizes the number of individuals with pre-AIDS HIV infection, balanced against the costs associated with PrEP. The author [12] develop a model of HIV risk and compare HIV-risk estimates before and after the introduction of PrEP to determine the maximum tolerated reductions in condom use with regular partners and clients for HIV risk not to change. Few mathematical studies have been undertaken to model Human Immunodeficiency Virus mathematically, but they did not considered drug resistance in their studies
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