Mathematical modeling and optimal control analysis of COVID-19 in Ethiopia

Abstract

In this paper, we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point(DFEP), basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagin’s Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.

Subject Classification: (2020):

• 34D08
• 34D20
• 34D23
• 49K10
• 49M05

Keywords:

• COVID-19
• Optimal control theory
• Modeling
• Ethiopia
• Numerical simulation