Dynamics and control of mpox disease using two modelling approaches

Abstract Monkeypox (Mpox) is a serious illness that affects both humans and animals. Two modelling approaches are considered here to understand the transmission dynamics of mpox. A deterministic model that incorporates the major factors that influence mpox is developed and analysed. However, as more than one group can be infected by mpox, humans and animals, the results of a deterministic model do not always hold when at the outset the number of people infected is small. Thus, a stochastic model based on the assumptions of the deterministic model is also developed and analysed. By fitting the deterministic model to data on the 2022 mpox outbreak in Nigeria, essential parameters related to the mpox dynamics are estimated. Using these parameters the basic reproduction number is calculated as $$\mathcal {R}_0 = 1.7$$ R 0 = 1.7 and, as this is greater than unity, implies that without control mpox is likely to remain endemic in Nigeria. Consideration of the basic reproduction number for the different transmission routes and parameter sensitivity analyses indicate the importance of animals in the overall prevalence of the disease. Also, numerical simulations are used and show that controls of disease transmission from animals to humans and animals to animals are the most effective. The results of the stochastic model, where the initial number of infections is small, show that the disease can be eradicated in some situations where $$\mathcal {R}_0 > 1$$ R 0 > 1 . However, the probabilities of this occurring for the Nigerian epidemic are low. Overall, our model formulations could be useful for making decisions on the effective management of mpox outbreaks in any endemic area.