Optimal control model for the infectiology of staphylococcus aureus with dual transmission pathways

Abstract

Staphylococcus aureus has been increasing globally, which negatively affects food safety, human and veterinary medicine. It colonizes about 30% of the world population, causing superficial skin and soft tissue infections. The dynamics of direct (human-to-human) and indirect (environment-to-human) transmission, shedding, and treatment failure of the disease remains an open epidemiological challenge. Therefore, this study introduces a mathematical model that incorporates both direct and indirect transmission cycle, effect of shedding, treatment failure and time-dependent control parameters. We derive an expression for the basic reproduction number, R0s, under different scenarios. Using comparison, Lyapunov and center manifold theories, we establish that the non-optimal control model is globally asymptotically stable whenever R0s<1 with a forward bifurcation diagram. The shedding of pathogens into the environment and dual transmission routes are the key determinants in the model that increased the number of colonized individuals. Optimal control model was exploring to unveil the impact of time-dependent hygiene practice, treatment and hydrogen peroxide for good human health and clean environment. We show also the control efficacies of the proposed intervention strategies. The key finding is that having triple controls (as in strategy 7) is better than having two controls (as in strategies 4–6) or a single control (as strategies 1–3), but economically very expensive. In a situation where two controls are the only available option, then the use of either improved hygiene practice and treatment (strategy 4) or treatment and hydrogen peroxide (strategy 6) be implemented for controlling staph infection in humans and environment. Whereas, in a case only one control is affordable, then optimized treatment is better than either improved hygiene practice or hydrogen peroxide. We hope that the outcomes of this study have presented policy-makers and decision-makers of low-, middle-and high-income countries with appropriate alternative interventions to implement while dealing with staph infections.