Dynamic Analysis and Optimal Control of COVID-19 with Comorbidity: A Modeling Study of Indonesia

Muhammad A. Rois¹, Fatmawati Fatmawati^1*, Cicik Alfiniyah¹ and Chidozie W. Chukwu²

• ¹Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Indonesia
• ²Department of Mathematics, College of Arts and Sciences, Wake Forest University, United States

Comorbidity is defined as the coexistence of two or more diseases in a person at the same time. The mathematical analysis of the COVID-19 model with comorbidities presented includes model validation of cumulative cases infected with COVID-19 from 1 November 2020 to 19 May 2021 in Indonesia, followed by positivity and boundedness solutions, equilibrium point, basic reproduction number, and stability of the equilibrium point. Sensitivity analysis was carried out to determine how the parameters affect the spread. Disease-free equilibrium points are asymptotically stable locally and globally if $R_0<1$ and endemic equilibrium points exist, locally and globally asymptotically stable if $R_0>1$. In addition, this disease is endemic in Indonesia, with a basic reproduction number of $R_0=1.47$. Furthermore, two optimal controls, namely public education and increased medical care, are included in the model to determine the best strategy to reduce the spread of the disease. Overall, the two control measures were equally effective in suppressing the spread of the disease as the number of COVID-19 infections was significantly reduced. So it was concluded that more attention should be paid to COVID-19 patients with underlying comorbid conditions because the probability of being infected with COVID-19 is higher and mortality in this population is much higher. Finally, the combined control strategy is an optimal strategy that provides an effective guarantee to protect the public from COVID-19 infection based on numerical simulations and cost evaluations.