Theoretical perspectives on the within-human host model for Lassa fever

Abstract

In this paper, we theoretically analyzed the within-human host model for Lassa fever earlier proposed by Obasi and Mbah, so as to understand the dynamics of Lassa fever transmission at the human population level. The model has locally asymptotically stable disease-free equilibrium whenever the associated reproduction number is less than unity. This model will undergo the phenomenon of backward bifurcation where the stable disease-free co-exists with a stable endemic equilibrium, when the associated reproduction number is less than unity. This implies that bringing down the reproduction number to below unity is not enough to eradicate Lassa fever disease within human population. It is also shown that the model has a globally-asymptotically stable disease-free equilibrium whenever the associated reproduction number is less than unity. The reproduction number, RWH<1, which is an important parameter in the control of Lassa fever infection, has been calculated using the next generation method. We have also shown that the endemic equilibrium point exists for RWN>1 and has been noted that this endemic equilibrium is unique and locally asymptotically stable based on Lyaponuv Function. However, this work has thrown up important parameters that could be gathered by the relevant government agencies for better understanding of the burden of Lassa fever disease in the human population.