A Co-infection Model for Monkeypox and HIV/AIDS: Sensitivity and Bifurcation Analyses

Monkeypox can make people very sick. The skin becomes infected with bacteria, thus causing severe skin damage. This can lead to corneal infection with loss of vision, pneumonia, difficulty swallowing, diarrhoea and vomiting leading to harsh malnutrition or dehydration, several organs inflammation or death. HIV-AIDS is a life-threatening and chronic condition. In HIV-infected individuals whose immune systems have been compromised, monkeypox mortality alone may be much higher. The co-infection of monkeypox and HIV/AIDS infections has been studied from a mathematical perspective by constructing a 13-compartment deterministic model. Basic mathematical analyses were performed on the co-infection model and the sub-models. The disease equilibrium points, the non-negativity of solutions, the basic reproduction numbers, the invariant region and the stability patterns. When the basic reproduction number is less than unity, the disease-free equilibrium points of each sub-model are globally asymptomatically stable. Certain calculations were done using the maple 18 programming language. The sensitivity analysis reveals that the parameters of the basic reproduction of the monkeypox sub-model with positive sensitivity indices are the probability of catching the monkeypox virus, the rate of effective contact, the compartment Im ’s coefficient of infection and the monkeypox vaccine’s waning rate, while the parameters of the basic reproduction of the HIV/AIDS sub-model with positive sensitivity indices are the probability of catching HIV virus, the rate effective contact, the compartment Ih ’s coefficient of infection and the compartment Ah ’s coefficient of infection. Via the centre manifold theorem, the bifurcation analysis reveals a forward bifurcation pattern for the monkeypox sub-model and the HIV/AIDS sub-model, and under a certain condition, a critical value of the monkeypox basic reproduction exists such that an effective management and possible elimination of the monkeypox infection would require that the monkeypox basic reproduction number should be kept below unity and above the critical value.