Mathematical Formulation of a Co-infection Model and its Analyses for Monkeypox and HIV/AIDS Infections

The dynamics of the co-infection of monkeypox and HIV/AIDS is examined from a mathematical perspective via a deterministic 13-compartment model. This consists of the investigation of the equilibrium points, the basic reproduction numbers and the equilibrium points’ stability. The mathematical analysis reveals that the model is epidemiologically well-posed, and that the basic reproduction number for the monkeypox sub-model is a function of the likelihood of getting infected, the rate of effective contact, the infection coefficient of the monkeypox-infectious class, the monkeypox prevention measure, the progression rate from monkeypox-exposed class to monkeypox-infectious class, the natural death rate, the vaccination rate and the waning rate of the vaccine. It also depends on the recovery rate for the monkeypox-exposed class and the monkeypox-induced death rate. The analysis also reveals that the basic reproduction number for the HIV/AIDS sub-model is a function of the likelihood of getting infected, the rate of effective contact, the HIV/AIDS prevention measure, the infection coefficient of the monkeypox-infectious class, the HIV/AIDS-induced death rate, the natural death rate, the infection coefficient of AIDS-only class, and the progression rate of HIV-only class to AIDS-only. The stability analysis reveals that the disease-free equilibrium of the sub-models are globally asymptomatically stable, when the basic reproduction number is less than unity. Numerical simulations of the model reveal the effect of changes in certain parameter values on the population sizes. Increasing or lowering the values of certain parameters can significantly affect the sizes of some classes. The Maple 18 programming software was used to carry out all calculations and numerical simulations.