African trypanosomiasis is a vector-borne disease that is mainly transmitted by infected tsetse flies. A deterministic model of tsetse fly vector, human, and cattle hosts is formulated and analyzed to gain insights into the disease dynamics. The roles of public health education, treatment, and tsetse fly traps are studied. The effective reproduction number, a threshold used to determine whether the disease persists or dies out in the population, is determined. The sensitivity analysis of the model parameters is performed to determine their relationship with the effective reproduction number. The results show that the tsetse fly biting rate is the most sensitive parameter to the effective reproduction number. Furthermore, the model’s numerical simulation shows that a combination of all three interventions has the most significant impact on the control of African trypanosomiasis. Thus, we recommend that these control measures be put concurrently in endemic areas for effective control of the disease transmission.

The COVID-19 pandemic began in Wuhan City in the Hubei province of China in December 2019. The disease spread quickly in many countries around the world due to mobility of people from one location to another. As a result, a COVID-19 mathematical model with the impacts on immigrants was proposed to study its transmission dynamics and possible control measures. The reproduction number was determined by using the next-generation technique and found to be 0.636, indicating that the transmission could be minimized in the community if all immigrants were effectively controlled. The Pontryagin's Maximum Principle was applied in analysing control strategies which are screening of immigrants, provision of public education to raise community awareness, and treatment of infected individuals. The simulated results revealed that a combination of public education, screening of all immigrants, and treatment of infected individuals plays a significant role in reducing COVID-19 transmission in the community. Keywords: COVID-19; Immigrants; Optimal control theory;

In this paper, one-strain tuberculosis (TB) model with two control mechanisms, education campaigns and chemoprophylaxis of TB-infected patients, was studied to determine their effects on the reduction of latent and active TB cases. In the case of analysis, boundedness and positivity of the model solutions were carried out to determine the biological feasibility of the study. Besides, the calibration of the parameters by utilizing the identifiability technique through the Markov chain Monte Carlo (MCMC) was thoroughly analysed. The optimum conditions for controlling TB were derived from the Pontryagin Maximum Principle. The numerical simulations were carried out using the forward-back sweep method with the help of the Runge-Kutta fourth-order numerical schemes. Simulation results showed that the education campaigns strategy is more effective in reducing TB infections than the chemoprophylaxis of TB-infected individuals. The combination of the two control strategies reduces a significant number of infections than when each strategy is used on its own. To minimize the transmission of TB from the community, we recommend the education campaigns strategy be a focal point and treatment of latent TB to be paired with the treatment of active TB cases. Keywords: Tuberculosis, Education campaigns, Chemoprophylaxis, MCMC

An optimal control model of African trypanosomiasis to minimize the cost of implementing control efforts and the number of infected humans, cattle, and tsetse-fly populations in their respective communities was formulated. Time-dependent controls such as public health education, human and cattle treatments, and tsetse-fly trapping were considered. Using Pontryagin’s maximum principle, the necessary conditions and the existence of an optimal control solution of an optimal control problem were analyzed. Using forward and backward in time fourth-order Runge–Kutta scheme, numerical simulations of the optimal control problem were performed. The results showed that the strategy involving public health education, treatment of humans, cattle treatment, and trapping of tsetse-flies was the most effective in reducing the number of infected individuals in their respective populations. Furthermore, the incremental cost-effectiveness analysis was performed, which showed that the tsetse-fly trapping was the most cost-effective strategy to implement in source limited settings.