In this research paper, we depict an unprecedented four-dimensional ordinary differential equation modeling the dynamic transmission of the Lassa fever virus incorporating relapse and reinfection rate. Recent studies showed that the recovered individuals from Lassa fever can again be susceptible; which contradicted the common assumptions made by different researchers on modeling of Lassa fever. So, this article corrects and states the implications of the assumptions on the population density. The numerical simulations unveil the effect of relapse, reinfection, and treatment rate in the affected population. Performing sensitivity analysis suggests all new incorporated parameters can impact the infection dynamics substantially. The stability analysis was carefully estimated where expression for each compartmentalized variable was calculated at both disease-free and persistence (endemic) equilibrium. Also, the basic reproduction number of the novel model was calculated using the Next Generation Matrix. The analytical results justify that the persistence (endemic) and the disease-free equilibrium are locally and globally asymptotically stable using both Routh Hurwitz Criterion and Comparison Theorem.
Keywords: Lassa fever, Reinfection rate, Relapse rate, Treatment rate, Sensitivity analysis.
Ebola virus is zoonotic. Earlier research has paid less attention to vector–host transmission dynamics of the virus. In this study, we, therefore, proposed an unprecedented coupled SEIR-SEI epidemic model of the type ShEhIhRh-SbEbIb which predicts the prevalence and virulence of the Ebola virus from bats to humans. More so, since remnants of the virus can still last for days in the fluidic parts of the body after recovery, the recovery class Rh is subdivided into two ( Rhis & Rhni). The sensitivity analysis investigation reveals parameters that have profound effects on the reproduction number. The system is proven to be positive and bounded at all times and the fundamental parameters for invasion, R0h and R0b for both human and bat populations respectively were established to be less than unity. Also, persistence (Endemic) and Disease Free Equilibrium points of the model were ascertained to be asymptotically stable both locally and globally.
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