title: Optimal control of HIV/AIDS in the workplace in the presence of careless individuals.
abstract: A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number, ℛ0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated when ℛ0 < 1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin's Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.
authors.affiliation: Applied Mathematics Department, Faculty of Mathematical Sciences, University for Development, Navrongo, Ghana.
authors.forename: Baba
authors.identifier: 0000-0001-5652-2690
authors.initials: B
authors.lastname: Seidu
authors.affiliation: Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa.
authors.forename: Oluwole D
authors.identifier: 0000-0003-4550-9591
authors.initials: OD
authors.lastname: Makinde
mesh_terms: D000163:Acquired Immunodeficiency Syndrome / Q000517:prevention & control* / Q000635:transmission*; D000465:Algorithms; D050936:Basic Reproduction Number; D003140:Communicable Disease Control / Q000379:methods*; D003198:Computer Simulation; D015658:HIV Infections / Q000517:prevention & control* / Q000635:transmission*; D006801:Humans; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D016273:Occupational Exposure; D016272:Occupational Health; D017132:Workplace
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