Bifurcation and Crossover Processes in the Dynamics of a Marburg Haemorrhagic Fever Model

Abstract

Just like Ebola disease, Marburg virus disease (MVD) remains a constant threat to people’s lives, not only in Africa, but also in other parts of the globe. Recorded past outbreaks have occurred in Europe, the Americas, and of course Africa, especially in places where inhabitants come into contact with wild animal products or live alongside wild animals such as apes, monkeys, and fruit bats on a daily basis. Therefore, studying the dynamics of the Marburg virus and conducting some epidemiological assessments remain relevant and important for preventing future outbreaks. In this paper, we analyze a Marburg epidemic model with nonlinear transmission. The well-posedness result is established, along with conditions for boundedness and dissipativity. Then, we intensively analyze the stability of the model’s equilibria. The bifurcation dynamics indicate the existence of both transcritical bifurcation (exchange of stability between the endemic equilibrium (EE) and the disease-free equilibrium (DFE)) and backward bifurcation, where the classical epidemiological condition for MVD to die out $(\mathcal{R}_0 < 1)$ is no longer sufficient, but remains necessary. Lastly, some numerical simulations show the convergence of trajectories to both the EE and the DFE. Some adequate preventive measures are provided.