We have proposed an unprecedented deterministic model of Lassa Haemorrhagic fever (LHF) model with nonlinear force of LHF infection to capture the transmission dynamics and long term effects of the disease. The Qualitative analyses we have conveyed on this model using well established methods viz: Cauchy’s differential theorem, Birkhoff & Rota’s theorem verifies and reveals the well-posedness, and carrying capacity of the model respectively. We established that a LHF-free equilibrium termed the disease-free equilibrium (DFE) exists for this model and this equilibrium however from our stability analyses, tends to be stable when the basic reproduction number computed via next generation matrix method is less than unity (one); and unstable if otherwise. Furthermore, we have carried out a sensitivity analyses to check variation effects of the model parameters when increased or decreased using the normalized forward-sensitivity index; unraveling the most sensitive parameters which requires the attention of the healthcare workers as; the effective contact rates W, and the rodents’ recruitment rate e. After which numerical simulations of the model were carried out to verify our qualitative analyses (Stability and sensitivity analysis) and to study the dynamical behavior of the model; showing that the presence of saturation instantaneously causes the system to approach a DFE/LHF-Free equilibrium.
From these qualitative analyses and numerical simulation results, we recommend early intervention and early treatment of Lassa haemorrhagic virus infection (LAHV) with Ribavirin on the infected, maximum hygiene practices and periodic evacuation of rodents in households in order to curb the recruitment of wild/rodents.