Abstract
The respiratory infectious disease Coronavirus Disease 2019 caused by the SARS-CoV-2 virus has become a world pandemic. This paper aims to develop a mathematical model of the spread of Covid-19 SEIQR (Susceptible-Exposed-Infected-Quarantine-Recovered), then analyse the stability of the model and its optimal control. Based on the local stability analysis using the Routh-Hurwitz criteria obtained two equilibrium points, namely the local asymptotically stable disease-free equilibrium points if reproduction number less than one and the local asymptotically stable endemic equilibrium point if reproduction number more than one. Next, to analyze global stability at the equilibrium points is used the Lyapunov method. Further, four controls, namely vaccination, physical distancing, treatment of infected individuals, and self-prevention (wearing masks and hand sanitisers) are applied to reduce the spread of covid-19. We applied Pontryagin’s Maximum Principle to obtain the optimal solution for the control. Finally, based on numerical result is found that the value of reproduction number is 9,44183. By using data from province of East Java, Indonesia, it is obtained that the physical distancing control has a better level effectiveness than the others three controls.
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