Epidemiological Implications of Vertical Transmission and Nonlinear Treatment in Lassa fever: A Mathematical Study

Abstract

Lassa fever is a viral hemorrhagic disease primarily transmitted through contact with food or household items contaminated by urine or feces of infected rodents. The disease poses a significant health risk in endemic regions, yet the effect of vertical transmission and non-linear treatment on its spread has not been thoroughly explored. To address this, a mathematical model was constructed to assess the effect of vertical transmission and non-linear treatment in the transmission dynamics of Lassa fever. The model was validated through the theory of positivity and boundedness, ensuring that its solution remains biologically meaningful over time. The existence of equilibrium points was examined and the basic reproduction number was calculated using the next generation matrix operator. Bifurcation analysis is performed using the Center Manifold Theory. The Local and global stability of the model around the Lassa fever free equilibrium is investigated using Jacobian Matrix method and the theorem proposed by Castillo-Chavez. The effect of the parameters of the basic reproduction number was investigated using normalized forward sensitivity index. Furthermore, it was inferred that decrease in the contact rate and the rate of vertical transmission were instrumental to curtailing the spread of Lassa fever in the population.