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

Abstract

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.