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.

A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac's criterion respectively.

In this paper, a deterministic mathematical model was proposed and analyzed to understand the dynamics of tuberculosis based on the SEIRS model. The disease-free equilibrium, the endemic equilibrium, and their stabilities were examined. The R0 (basic reproduction number) was derived using the Next Generation Matrix method and its sensitivity analysis showed that the birth rate and infectious rate were the most sensitive parameters of R0. The behaviour of exposed individuals at the latent period with varied treatment rates were examined through numerical simulation. From the analysis carried out, the effect of variations of the treatments of latent TB shows that it affects the disease burden. This implies that testing and treatment of latent TB are important in preventing it from becoming infectious. The re-infection rate was examined to see the effect it had both on the recovered and susceptible populations. The study concludes by recommending the extension of the model to an age structured model with co-infection with another respiratory infectious disease like COVID-19. Keywords: Epidemiology; Latent TB treatment; Basic Reproduction Number; sensitivity analysis; numerical simulation