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SARS-CoV-2 Disease in Cameroon: Theoretical and Computational Analysis of a Delayed SIQR Model with Optimal Control
27 Pages Posted: 20 Oct 2022 Publication Status: Preprint
Abstract
We investigate a SIQR mathematical model of COVID-19 in Cameroon (Central Africa) taking into account the vaccination and treatment effects. The model is described in terms of a system of four ordinary nonlinear equations describing the time evolution of susceptible, infectious, quarantine and recovered humans. It takes also into account time delay effects in the state, vaccination and treatment. We use the Pontryagin’s maximum principle to investigate the control model with delays in the state and control (vaccination and treatment). We perform the numerical simulations of the model by using a forward and backward finite difference algorithm for reported case data of COVID-19 in Cameroon from October 01, 2021 to January 01, 2022. We investigate numerically the evolution of the disease under the influence of optimal control between January 1, 2022 and December 31, 2022. We analyse and compare the basic reproduction number R 0 in the case without control and with control. The results show that, without control R 0 = 3.94, and in the presence of control strategy R 0 = 0.05. It is also numerically confirmed that when the efficacy increases, the number of infected humans decreases. The control strategy is more effective when combining vaccination and treatment. The obtained results may excite the Cameroon Public Health Ministry to better organise the strategy to eradicate the COVID-19 disease in Cameroon by intensifying public health interventions.
Funding Information: None.
Declaration of Interests: None.
Keywords: COVID-19, Time delay, optimal control, SIQR model
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