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Non Pharmaceutical Interventions for Optimal Control of COVID-19.
Comput Methods Programs Biomed. 2020 Nov; 196:105642.CM

Abstract

BACKGROUND AND OBJECTIVE

The 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.

METHODS

To 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.

RESULTS

We 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.

CONCLUSION

We 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.

Links

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Authors+Show Affiliations

Zamir M
Department of Mathematics, University of Science and Technology Bannu, Khyber Pakhtunkhwa, Pakistan.
Shah Z
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand. Electronic address: zahir.sha@kmutt.ac.th.
Nadeem F
Department of Mathematics, University of Science and Technology Bannu, Khyber Pakhtunkhwa, Pakistan.
Memood A
Department of Mathematics and Statistics, Riphah International University Sector I-14, Islamabad, Pakistan.
Alrabaiah H
College of Engineering, Al Ain University, Al Ain 64141, UAE; Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan.
Kumam P
KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan. Electronic address: poom.kum@kmutt.ac.th.

MeSH

AlgorithmsBasic Reproduction NumberBetacoronavirusCOVID-19COVID-19 TestingClinical Laboratory TechniquesCommunicable Disease ControlComputer SimulationCoronavirus InfectionsDisease OutbreaksHand DisinfectionHumansMasksModels, TheoreticalPandemicsPersonal Protective EquipmentPneumonia, ViralSARS-CoV-2Social Isolation

Pub Type(s)

Journal Article

Language

eng

PubMed ID

32688137

Citation

Zamir, Muhmmad, et al. "Non Pharmaceutical Interventions for Optimal Control of COVID-19." Computer Methods and Programs in Biomedicine, vol. 196, 2020, p. 105642.
Zamir M, Shah Z, Nadeem F, et al. Non Pharmaceutical Interventions for Optimal Control of COVID-19. Comput Methods Programs Biomed. 2020;196:105642.
Zamir, M., Shah, Z., Nadeem, F., Memood, A., Alrabaiah, H., & Kumam, P. (2020). Non Pharmaceutical Interventions for Optimal Control of COVID-19. Computer Methods and Programs in Biomedicine, 196, 105642. https://doi.org/10.1016/j.cmpb.2020.105642
Zamir M, et al. Non Pharmaceutical Interventions for Optimal Control of COVID-19. Comput Methods Programs Biomed. 2020;196:105642. PubMed PMID: 32688137.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Non Pharmaceutical Interventions for Optimal Control of COVID-19. AU - Zamir,Muhmmad, AU - Shah,Zahir, AU - Nadeem,Fawad, AU - Memood,Arif, AU - Alrabaiah,Hussam, AU - Kumam,Poom, Y1 - 2020/07/07/ PY - 2020/05/18/received PY - 2020/06/29/accepted PY - 2020/7/21/pubmed PY - 2020/11/11/medline PY - 2020/7/21/entrez KW - Basic reproduction number KW - Mathematical model KW - Next generation matrix KW - Novel coronavirus KW - Optimal control KW - Pontryagin’s Maximum Principle KW - Sensitivity analysis SP - 105642 EP - 105642 JF - Computer methods and programs in biomedicine JO - Comput Methods Programs Biomed VL - 196 N2 - BACKGROUND AND OBJECTIVE: The 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. METHODS: To 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. RESULTS: We 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. CONCLUSION: We 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. SN - 1872-7565 UR - https://www.unboundmedicine.com/medline/citation/32688137/Non_Pharmaceutical_Interventions_for_Optimal_Control_of_COVID_19_ DB - PRIME DP - Unbound Medicine ER -