Population dynamics of a mathematical model for Monkeypox - Ashezua∗†, T.T.; Gweryina†‡, R.I.; Kaduna†§, F.S. (International Journal of Mathematical Analysis and Modelling, 2023)
Monkeypox, a zoonotic disease, is gradually posing a public health challenge to both developed and developing countries of the world. To this end, there is need to come up with prevention and control strategies to help curb the spread of the disease in the population. In this study, a new deterministic mathematical model for monkeypox is developed to critically look at the impact of public awareness campaign, treatment and vaccination on the transmission dynamics, prevention and control of monkeypox. Qualitative analysis of the model shows that it undergoes the phenomenon of backward bifurcation. However, this phenomenon may not occur as a results of the non-availability of monkeypox vaccine in the community. Furthermore, the model is shown to have three endemic equilibria, namely: the human-to-human, animal-to-human and animal-to-animal transmission modes, respectively, when the associated reproduction number is greater than unity. For the special case, where there is only human-to-human transmission of monkeypox (i.e. υ = ω = φ = βa = 0), the disease-free equilibrium of the model is shown to be globally asymptotically stable (GAS) whenever the associated reproduction number is less than unity. For the same scenario as above, the unique endemic equilibrium of the model is globally asymptotically stable whenever the reproduction number is greater than unity. Both analytical and numerical results show a relationship between the rate of vaccination of the susceptible individuals, the progression rate from the exposed stage of infection to the asymptomatic and symptomatic stages of infection, treatment rate of the symptomatic individuals, public awareness campaign and the reproduction number. Results from the sensitivity analysis of the model, using the human reproduction number number, R0h, show that, the most sensitive parameters are the monkeypox transmission rate from human-to-human (βh), efficacy of public awareness campaign (ψ), vaccination rate for the susceptible individuals (υ), waning rate of the monkeypox vaccine (ω) and the treatment rate for the symptomatic individuals (τ). The epidemiological implication of these results is that, public awareness campaign in the population should be strengthened by the government and other critical stakeholders in order to educate the populace on the need to be vaccinated against monkeypox infection, get to a health facility immediately when blisters show up on their body and the need to develop vaccines that will not wane within a short period of time. Numerical simulations results show that, increasing the rates of vaccination of the susceptible individuals, efficacy of public awareness campaign and the treatment of symptomatic individuals could help in reducing monkey pox burden in the population.