A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic
In this paper, we propose a mathematical model to assess the impacts of using face masks, hospitalization of symptomatic individuals and quarantine of asymptomatic individuals in combating the COVID-19 pandemic in India. We calibrate the proposed model to fit the four data sets, viz. data for the st...
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doaj-80340c071ebe449e88db78b4955ae4082021-04-02T02:43:24ZengAIMS PressMathematical Biosciences and Engineering1551-00182021-04-0118118221310.3934/mbe.2021010A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochasticAkhil Kumar Srivastav0Pankaj Kumar Tiwari 1Prashant K Srivastava2Mini Ghosh3Yun Kang41. Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India2. Department of Mathematics, University of Kalyani, Kalyani - 741235, India3. Department of Mathematics, Indian Institute of Technology Patna, Patna - 801103, India1. Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, IndiaScience and Mathematics Faculty, Arizona State University Mesa, AZ 85212, USAIn this paper, we propose a mathematical model to assess the impacts of using face masks, hospitalization of symptomatic individuals and quarantine of asymptomatic individuals in combating the COVID-19 pandemic in India. We calibrate the proposed model to fit the four data sets, viz. data for the states of Maharashtra, Delhi, Tamil Nadu and overall India, and estimate the rate of infection of susceptible with symptomatic population and recovery rate of quarantined individuals. We also estimate basic reproduction number to illustrate the epidemiological status of the regions under study. Our simulations infer that the infective population will be on increasing curve for Maharashtra and India, and settling for Tamil Nadu and Delhi. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected individuals. Our results reveal that to curtail the disease burden in India, specific control strategies should be implemented effectively so that the basic reproduction number is decreased below unity. The three control strategies are shown to be important preventive measures to lower disease transmission rate. The model is further extended to its stochastic counterpart to encapsulate the variation or uncertainty observed in the disease transmissibility. We observe the variability in the infective population and found their distribution at certain fixed time, which shows that for small populations, the stochasticity will play an important role.http://www.aimspress.com/article/doi/10.3934/mbe.2021010?viewType=HTMLcovid-19deterministic and stochastic modelface maskhospitalizationquarantineparameter estimationsensitivity analysis |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Akhil Kumar Srivastav Pankaj Kumar Tiwari Prashant K Srivastava Mini Ghosh Yun Kang |
spellingShingle |
Akhil Kumar Srivastav Pankaj Kumar Tiwari Prashant K Srivastava Mini Ghosh Yun Kang A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic Mathematical Biosciences and Engineering covid-19 deterministic and stochastic model face mask hospitalization quarantine parameter estimation sensitivity analysis |
author_facet |
Akhil Kumar Srivastav Pankaj Kumar Tiwari Prashant K Srivastava Mini Ghosh Yun Kang |
author_sort |
Akhil Kumar Srivastav |
title |
A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic |
title_short |
A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic |
title_full |
A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic |
title_fullStr |
A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic |
title_full_unstemmed |
A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic |
title_sort |
mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of covid-19 in india: deterministic vs. stochastic |
publisher |
AIMS Press |
series |
Mathematical Biosciences and Engineering |
issn |
1551-0018 |
publishDate |
2021-04-01 |
description |
In this paper, we propose a mathematical model to assess the impacts of using face masks, hospitalization of symptomatic individuals and quarantine of asymptomatic individuals in combating the COVID-19 pandemic in India. We calibrate the proposed model to fit the four data sets, viz. data for the states of Maharashtra, Delhi, Tamil Nadu and overall India, and estimate the rate of infection of susceptible with symptomatic population and recovery rate of quarantined individuals. We also estimate basic reproduction number to illustrate the epidemiological status of the regions under study. Our simulations infer that the infective population will be on increasing curve for Maharashtra and India, and settling for Tamil Nadu and Delhi. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected individuals. Our results reveal that to curtail the disease burden in India, specific control strategies should be implemented effectively so that the basic reproduction number is decreased below unity. The three control strategies are shown to be important preventive measures to lower disease transmission rate. The model is further extended to its stochastic counterpart to encapsulate the variation or uncertainty observed in the disease transmissibility. We observe the variability in the infective population and found their distribution at certain fixed time, which shows that for small populations, the stochasticity will play an important role. |
topic |
covid-19 deterministic and stochastic model face mask hospitalization quarantine parameter estimation sensitivity analysis |
url |
http://www.aimspress.com/article/doi/10.3934/mbe.2021010?viewType=HTML |
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