Modelling the Impacts of Immigrants on COVID 19 Transmission Dynamics with Control Measures

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

Application of optimal control to tuberculosis model with parameter estimations: Bayesian approach

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, MCM