Mathematical analysis of Lassa fever epidemic model utilizing Nigeria demographic data

In this paper, we proposed and analysed a non-linear deterministic mathematical model for the transmission dynamics of Lassa fever virus in Nigeria. The basic properties of the model are presented. For the linear stability of the model equilibria the basic reproduction number $R_0$ and other important threshold parameters associated with existence and stability of endemic state are obtained. We showed that the model exhibits two equilibrium points namely: the Lassa fever-free equilibrium point and the endemic equilibrium point. The Lassa fever-free equilibrium $\tilde{\Sigma }$ is the only local asymptotic stable equilibrium if the threshold parameter in relation to humans, $R_{0h}<1$ and it is not stable when $R_{0h}>1$. While the endemic equilibrium point ${\Sigma }^{\ast }$ becomes asymptotically stable locally under certain conditions on the associated threshold parameters. Sensitivity analysis of the model parameters indicates that the natural mortality rate of rodents ($\psi$) and the effective contact rate of rodents (${\beta }_3$)are the basic control parameters associated with persistence or eradication of Lassa fever virus. More precisely, there is an inverse relationship between $R_0$ and $\psi$ so that an increase of the latter leads to the decrease of the former one and vice-versa. In a similar note, increasing (decreasing) the value of ${\beta }_3$ keeping all other parameters fixed increases (decreases) the value of $R_0$. We can infer from this result that good environmental sanitation and fumigation would reduce rodents’ population thereby reducing the value of ${\beta }_3$ which leads to the decrease of $R_0$.