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 government 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 non-pharmacological 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 was computed with and without interventions and was 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 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 the virus to the barest minimum.

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

“…Also when the objective function is defined as a linear combination of the quadratic terms of control variables the complexity of the problem reduces. Studies where objective function is considered as a linear combination of the quadratic terms of control variables can be found in [32,39]. The integrand of the cost function (6.1), denoted by is called the Lagrangian or the running cost.…”

Prediction of Covid-19 spreading and optimal coordination of counter-measures: From microscopic to macroscopic models to Pareto fronts

“…There is a variety of ODE models for describing Covid-19 spreading, many of them built on the idea behind the SIRD model but extending it by adding categories, e.g., [19,22,26,29,40], or by considering other compartmental variants [27]. Other approaches utilize delay differential equations (DDE) [11] or stochastic models, either in the form of stochastic differential equations [41], in discrete form [16] or by probabilistic means [12].…”

“…We only claim the novelty of the combined strategy (A)-(C). Recent literature contains a variety of approaches on optimal control of Covid-19 spreading, see, e.g., [19,22,26,29], with the underlying idea being even older and more general [14]. Some parts from these approaches could also be included in the framework presented in this paper, however, we focus on our core ideas for now to make clear where the novelty lies.…”

Robust optimal control of compartmental models in epidemiology: Application to the COVID-19 pandemic

“…In [27] , a COVID-19 disease spread model with free terminal optimal time is defined in which the goal is to reduce the size of susceptible, infected, exposed, and asymptomatic groups in order to consequently eradicate the infection by using quarantine and treatment of infected people. In [28] , the effects of non-pharmacological strategies such as quarantine, isolation, and public health education are studied as time-dependent interventions to ascertain their contributions to the transmission dynamics of COVID-19. Optimal control strategies for the Zika infection with mutations that cause defects in the newly birth for infected pregnant woman are formulated in [29] .…”