A non-linear mathematical model for analysing the impact of COVID-19 disease on higher education in developing countries.

This study proposes a non-linear mathematical model for analysing the effect of COVID-19 dynamics on the student population in higher education institutions. The theory of positivity and boundedness of solution is used to investigate the well-posedness of the model. The disease-free equilibrium solution is examined analytically. The next-generation operator method calculates the basic reproduction number (R0). Sensitivity analyses are carried out to determine the relative importance of the model parameters in spreading COVID-19. In light of the sensitivity analysis results, the model is further extended to an optimal control problem by introducing four time-dependent control variables: personal protective measures, quarantine (or self-isolation), treatment, and management measures to mitigate the community spread of COVID-19 in the population. Simulations evaluate the effects of different combinations of the control variables in minimizing COVID-19 infection. Moreover, a cost-effectiveness analysis is conducted to ascertain the most effective and least expensive strategy for preventing and controlling the spread of COVID-19 with limited resources in the student population.

ON THE FRACTIONAL-ORDER MODELING OF COVID-19 DYNAMICS IN A POPULATION WITH LIMITED RESOURCES

Resource availability plays a pivotal role in the fight against emerging infections such as COVID-19. In the event where there are limited resources the control of an epidemic disease tends to be slow and the disease spread faster in the human population. In this paper, we are motivated to formulate and investigate a mathematical model via the Caputo derivative which incorporates the impact of limited resources on COVID-19 transmission dynamics in the population. We analyze the fractional model by computing the equilibrium points, and basic reproduction number, (R0), and also used the Banach-fixed point theorem to prove the existence and uniqueness of the solution of the model. The impact of each parameter on the dynamical spread of COVID-19 was examined by the help of Sensitivity analysis. Results from mathematical analyses depict that the disease-free equilibrium is stable if R0 < 1 and unstable otherwise. Numerical simulations were carried out at different fractional order derivatives to understand the impact of several model parameters on the dynamics of the infection which can be used to establish the influential parameter driving the epidemic transmission path. Our numerical results show that an increase in the recovery rate of hospitalization increases the number of infected individuals. The results of this work can help policymakers to devise strategies to reduce the COVID-19 infection. © 2023, SCIK Publishing Corporation. All rights reserved.