Mathematical Modelling and Analysis of Lassa fever Dynamics with Environmental Transmission and Reinfection

Abstract

A deterministic model with a variable human population, rodent population, and Lassa virus in the environment is presented and rigorously analyzed.

The model analysis showed a process known as backward bifurcation where the Lassa fever-free equilibrium (Disease-free) coexists with Lassa fever present (Endemic equilibrium point) when the threshold parameter $R_c$ is below one. The existence resulted from humans who had earlier recovered from Lassa fever being infected again with the Lassa virus when exposed continuously to the virus through environmental sources, close contact with infected individuals, and infected rodents. This result means, that having the threshold parameter $R_c$ below one does not guarantee total eradication of the menace.

Further investigation showed that backward bifurcation could be eliminated in the absence of reinfection. As a result, the global stability of the disease-free equilibrium is guaranteed when the threshold parameter $R_c$ is below unity.

Moreover, using a quadratic Lyapunov function, it is discovered that the unique endemic equilibrium is globally asymptotically stable.

Numerical analysis revealed the impacts of reinfection and other important parameters on the transmission of the disease. The analysis not only gave a thorough knowledge of the transmission but also justified the analytical results.