Controlling the Spread of COVID-19: Optimal Control Analysis

Abstract

Coronavirus disease 2019 (COVID-19) is a disease caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV-2). It was declared on March 11, 2020, by the World Health Organization as pandemic disease. The disease has neither approved medicine nor vaccine and has made governments and scholars search for drastic measures in combating the pandemic. Regrettably, the spread of the virus and mortality due to COVID-19 has continued to increase daily. Hence, it is imperative to control the spread of the disease particularly using nonpharmacological strategies such as quarantine, isolation, and public health education. This work studied the effect of these different control strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contributions in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number and effective reproduction numbers were computed with and without interventions, respectively, and were used to carry out the sensitivity analysis that identified the critical parameters contributing to the spread of COVID-19. The optimal control analysis was carried out using the Pontryagin’s maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings of the optimal control analysis and numerical simulations revealed that time-dependent interventions reduced the number of exposed and infected individuals compared to time-independent interventions. These interventions were time-bound and best implemented within the first 100 days of the outbreak. Again, the combined implementation of only two of these interventions produced a good result in reducing infection in the population. While, the combined implementation of all three interventions performed better, even though zero infection was not achieved in the population. This implied that multiple interventions need to be deployed early in order to reduce the virus to the barest minimum.

A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen

“…Equation (12) describes the environmental free bacteria. It is increased by the infected individuals at a rate of ξ , where humans can release bacteria into the open environment.…”

“…Dozens of mathematical models have been proposed to control the dynamics of the COVID-19 pandemic. Madubueze in [12] updated the SEQIHR (susceptible-exposed-quarantinedinfected-hospitalized-recovered) model to include new parameters reflecting the impact of health education, quarantine, and isolation. These parameters were used to determine the optimal control and to find the minimum cost associated with each control.…”

COVID-19 optimal vaccination policies: a modeling study on efficacy, natural and vaccine-induced immunity responses

“…Optimal control theory has also been used in COVID-19 studies. Most efforts have been invested in finding optimal strategies to evaluate the impact of non-pharmaceutical interventions [19][20][21]. Optimal control strategies have also being considered in vaccination strategies [22].…”

Assessment of Three Mathematical Prediction Models for Forecasting the COVID-19 Outbreak in Iran and Turkey

“…For this purpose, numerous prediction models have been proposed in the literature, which may be categorized into mathematical models [ 4 – 7 ] and soft computing approaches [ 3 , 8 , 9 ]. The former has many different types including simple explicit equations to a complicated system of equations with many parameters required to be calibrated.…”