Lassa fever is a zoonotic disease spread by infected rodents known as multimammate rats. The disease has posed a significant and major health challenge in West African countries, including Nigeria. To have a deeper understanding of Lassa fever epidemiology in Nigeria, we present a deterministic dynamical model to study its dynamical transmission behavior in the population. To mimic the disease’s biological history, we divide the population into two groups: humans and rodents. We established the quantity known as reproduction number $${\mathcal {R}}_{0}$$R 0 . The results show that if $${\mathcal {R}}_{0} <1$$R 0 < 1 then the system is stable, otherwise it is unstable. The model fitting was performed using the nonlinear least square method on cumulative reported cases from Nigeria between 2018 and 2020 to obtain the best fit that describes the dynamics of this disease in Nigeria. In addition, sensitivity analysis was performed, and the numerical solution of the system was derived using an iterative scheme, the fifth-order Runge–Kutta method. Using different numeric values for each parameter, we investigate the effect of all highest sensitivity indices’ parameters on the population of infected humans and infected rodents. Our findings indicate that any control strategies and methods that reduce rodent populations and the risk of transmission from rodents to humans and rodents would aid in the population’s control of Lassa fever.

Lassa fever is an infectious and zoonotic disease with incidence ranging between a hundred to three hundred thousand cases, with approximately five thousand deaths reported yearly in West Africa. This disease has become endemic in the Lassa belt of Sub-Saharan Africa, thus increasing the health burden in these regions including Nigeria. A deterministic mathematical model is presented to study the dynamics of Lassa fever in Nigeria. The model describes the transmission between two interacting hosts, namely the human and rodent populations. Using the cumulative number of cases reported by the Nigerian Centre for Disease Control within the first week of January 2020 through the eleventh week in 2021, we performed the model fitting and parameterization using the nonlinear least square method. The reproduction number $${\mathcal {R}}_{0}$$R 0 which measures the potential spread of Lassa fever in the population is used to investigate the local and global stability of the system. The result shows that the model system is locally and globally asymptomatically stable whenever $${\mathcal {R}}_{0}<1$$R 0 < 1 , otherwise it is unstable. Furthermore, the endemic equilibrium stability is investigated and the criteria for the existence of the phenomenon of bifurcation is presented. We performed the sensitivity analysis of each reproduction number parameter and solutions of the developed model are derived through an iterative numerical technique, a six-stage fifth-order Runge–Kutta method. Numerical simulations of the total infected human population $$(E_{h}+I_{h})$$( E h + I h ) under different numerical values (controlled parameters) are presented. The result from this study shows that combined controlled parameters made the total infected human population decline faster and thus reduces Lassa fever’s burden on the population.

Tuberculosis (TB) remains a formidable global health challenge, demanding effective control strategies to alleviate its burden. In this study, we introduce a comprehensive mathematical model to unravel the intricate dynamics of TB transmission and assess the efficacy and cost-effectiveness of diverse intervention strategies. Our model meticulously categorizes the total population into seven distinct compartments, encompassing susceptibility, vaccination, diagnosed infectious, undiagnosed infectious, hospitalized, and recovered individuals. Factors such as susceptible individual recruitment, the impact of vaccination, immunity loss, and the nuanced dynamics of transmission between compartments are considered. Notably, we compute the basic reproduction number, providing a quantitative measure of TB transmission potential. Through this comprehensive model, our study aims to offer valuable insights into optimal control measures for TB prevention and control, contributing to the ongoing global efforts to combat this pressing health challenge.

A Mathematical model of (S,E,I_u,I_d,I_s,R,D) is presented to study the dynamical spread of Ebola in the population. Existence of the Local Stability of the disease–free equilibrium (DFE) was investigated via the threshold parameter (Reproduction number R₀ ) obtained using the next generation matrix technique. The result shows that the DFE is asymptotically stable at Reproduction number less than unity (R_{0 < 1)}. Reasonable sets of values for the parameter in the model were compiled from existing literatures and Sensitivity analysis indices R₀ around the baseline parameter value were computed, which shows that the most sensitive parameter to R₀ is the recruitment rate π followed by the rate at which exposed individuals are isolated due to contact tracing σ. Furthermore, the numerical computation of R₀ gave a value of 0.16, and numerical simulation was obtained which illustrates the effect of control parameters on the various compartments of the model.