Sensitivity Analysis and Optimal Control of Covid 19 Model

Firmansyah Firmansyah, Yulita Molliq Rangkuti


Coronavirus infection is a disease that causes death and threatens human life; for prevention, it is necessary to quarantine susceptible, exposed, and infected populations and vaccinate the entire population. This kind of quarantine and vaccination is intended to reduce the spread of coronavirus. Epidemiological models are a strategy used by public health practitioners to prevent and fight diseases. However, to be used in decision making, mathematical models must be carefully parameterized and validated using epidemiological and entomological data. Epidemiological models: susceptible, symptomatic, contagious, and recovering. In this study, sensitivity analysis and optimal control were performed to determine the relative importance of the model parameters and to minimize the number of infected populations and control measures against the spread of the disease. Sensitivity analysis was carried out using a sensitivity index to measure the relative change in the basic reproduction number for each parameter, and this control function was applied to the dynamic modeling of the spread of COVID-19 using the Pontryagin Minimum Principle. We will describe the formulation of a dynamic system for the spread of COVID-19 with optimal control and then use Pontryagin’s Minimum Principle to find optimal control solutions. In this article, COVID-19 cases in the USA and India serve as examples of the efficiency of control measures. The results obtained revealed that the parameters that became the basis for reducing the number of infected with COVID-19 for the two countries, the USA and India, are effective transmission rates from S to E, (β), transmission rates from E to I, (α), and transmission rates from S to R, (ps), which are the main parameters to watch for growth with respect to Basic Reproduction rates (R0). Finally, three controls were simulated in cases I (in the USA) and II (in India) in the interval t ∈ [0, 15]. For all controls, the effectiveness was close to 50% in India and 100% in the USA to reduce the spread of COVID 19. According to the findings, if these three controls were implemented ideally from the start of the pandemic, the number of sufferers.


COVID-19; SEIR Model; Optimal Control; Sensitivity Analysis; Forward-Backward Sweep Method

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