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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.

SUBMITTER: Madubueze CE

PROVIDER: S-EPMC7499329 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Controlling the Spread of COVID-19: Optimal Control Analysis.

Madubueze Chinwendu E CE Dachollom Sambo S Onwubuya Isaac Obiajulu IO

Computational and mathematical methods in medicine 20200917

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 spre ...[more]

PMID: 32963585

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Project description:Background and objectiveThe outbreak of the current pandemic begun from the first individual of a 55-year old from Hubei province in China, the disease instigated by the new coronavirus spreading across the world. Scientists presently speculate this coronavirus, SARS-CoV-2, originated in a bat and by one way or another jumped to another creature, potentially the pangolin, which at that point gave it to people. The ailment is currently spreading between individuals with no animal delegate. Researchers are struggling to follow the infection back to where it started to become familiar with its spread. In the event that, for example, specialists can locate the soonest cases, they might have the option to distinguish the creature have where the infection hides. In March and April 2020, researchers detailed that this virus created normally. Coronavirus has been become of the serious global phenomena in the recent years and has negative effects in the entire world health and economy. The virus is believed to have been associated with a host animal which human contracted. Subsequently, human-to-human infection began. Through migration as humans have become complex with easy mobility the disease has traveled to the entire continent. Now, numerous scientist are going on in the hope of obtaining medication and vaccination to prevent the spread of the disease and mortality of the disease. It is important that we obtain quantitative and qualitative information about the etiology of this disease which is crucial. Mathematical modeling is capable of providing qualitative information on many parameters that guides the decision making of health practitioners. In this work we focus the optimal control of COVID-19 with the help of Non Pharmaceutical Interventions (NPIs). To find the role of factors/parameters in the transmission of the syndrome we find R0; the ratio of reproduction for the proposed model.MethodsTo find the role of parameters in the transmission of the syndrome we find R0; the ratio of reproduction for the proposed model. On the basis of sensitivity indices of the parameters we apply Non Pharmaceutical Interventions(NPIs) to control the sensitive parameters and hence formulate the optimal control mode. With the help of Hamiltonian and Lagrangian we minimize the density of contaminated stuff and infected human population.ResultsWe focus the optimal control of COVID-19 with the help of Non Pharmaceutical Interventions(NPIs). On the basis of sensitivity indices of the parameters we apply Non Pharmaceutical Interventions(NPIs) to control the sensitive parameters and hence formulate the optimal control model. The major NPIs are, STAY HOME, SANITIZER (wash hands), EARLY CASE DETECTION (PCR Test) and FACE MASK. These NPIs helps in mitigation and reducing the size of outbreak of the disease.ConclusionWe check the existence of the optimal solution for the system. At the end, Using matlab we produce numerical simulations for validation of results of control variables. The results demonstrate that if there is no control (variables/interventios), 900 out 1000 susceptible individuals may be infected (exposed) in very short period. As such a circumstances no agency fighting against COVID-19 could be successful due to its limited resources.

Project description:BackgroundThe word 'pandemic' conjures dystopian images of bodies stacked in the streets and societies on the brink of collapse. Despite this frightening picture, denialism and noncompliance with public health measures are common in the historical record, for example during the 1918 Influenza pandemic or the 2015 Ebola epidemic. The unique characteristics of SARS-CoV-2-its high basic reproduction number (R0), time-limited natural immunity and considerable potential for asymptomatic spread-exacerbate the public health repercussions of noncompliance with interventions (such as vaccines and masks) to limit disease transmission. Our work explores the rationality and impact of noncompliance with measures aimed at limiting the spread of SARS-CoV-2.MethodsIn this work, we used game theory to explore when noncompliance confers a perceived benefit to individuals. We then used epidemiological modeling to predict the impact of noncompliance on control of SARS-CoV-2, demonstrating that the presence of a noncompliant subpopulation prevents suppression of disease spread.ResultsOur modeling demonstrates that noncompliance is a Nash equilibrium under a broad set of conditions and that the existence of a noncompliant population can result in extensive endemic disease in the long-term after a return to pre-pandemic social and economic activity. Endemic disease poses a threat for both compliant and noncompliant individuals; all community members are protected if complete suppression is achieved, which is only possible with a high degree of compliance. For interventions that are highly effective at preventing disease spread, however, the consequences of noncompliance are borne disproportionately by noncompliant individuals.ConclusionsIn sum, our work demonstrates the limits of free-market approaches to compliance with disease control measures during a pandemic. The act of noncompliance with disease intervention measures creates a negative externality, rendering suppression of SARS-CoV-2 spread ineffective. Our work underscores the importance of developing effective strategies for prophylaxis through public health measures aimed at complete suppression and the need to focus on compliance at a population level.

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Controlling the Spread of COVID-19: Optimal Control Analysis.

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Controlling the Spread of COVID-19: Optimal Control Analysis.

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