# An Optimal Control of SIRS Model with Limited Medical Resources and Reinfection Problems

## Authors

• Amer M. Salman School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
• Mohd Hafiz Mohd School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
• Noor Atinah Ahmed School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
• Kamarul Imaran Musa School of Medical Sciences, Health Campus, Universiti Sains Malaysia, 16150 Kubang Kerian
• Issam Ahmed School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
• Zuhur Alqahtani Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahmen University, Riyadh, Saudi Arabia

## Keywords:

SIRS, optimal control, vaccination, limited medical resources, reinfection,

## Abstract

COVID-19 is a global public health problem that causes severe acute respiratory syndrome (SARS). It is also extremely contagious with rapidly increasing death rates. In this paper, we propose an optimal control model with SIRS (Susceptible–Infected–Recovered- Susceptible) kinetics to examine the effects of several intervention measures (e.g., vaccination and treatment) under the limited medical resources scenarios. This model is also employed to investigate the possibility of reinfection because of the fading of immunity problem. As a case study, the modeling framework is parametrised using COVID-19 daily confirmed and recovered cases in Malaysia. The parameters have been approximated by relying on the model's best fit to actual data published by the Malaysian Ministry of Health (MOH). Our numerical simulation results show that the inclusion of optimal control components with vaccination and treatment strategies would dramatically reduce the number of active cases even in the presence of reinfection forces. Regardless of the relative weightage (or costs) of vaccination and treatment, as well as the possibility of reinfection, it is critical to plan effective COVID-19 control measures by vaccinating as many people as possible (and as early as possible). Overall, these insights help explore the importance of intervention measures and the allocation of medical resources to control the severity of this pandemic.

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