A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic

Akhil Kumar Srivastav; Pankaj Kumar Tiwari; Prashant K Srivastava; Mini Ghosh; Yun Kang; Akhil Kumar Srivastav; Pankaj Kumar Tiwari; Prashant K Srivastava; Mini Ghosh; Yun Kang

doi:10.3934/mbe.2021010

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 182-213. doi: 10.3934/mbe.2021010

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A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic

1.
Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India
2.
Department of Mathematics, University of Kalyani, Kalyani - 741235, India
3.
Department of Mathematics, Indian Institute of Technology Patna, Patna - 801103, India
4.
Science and Mathematics Faculty, Arizona State University Mesa, AZ 85212, USA

Received: 31 August 2020 Accepted: 16 November 2020 Published: 26 November 2020

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.
- COVID-19,
- deterministic and stochastic model,
- face mask,
- hospitalization,
- quarantine,
- parameter estimation,
- sensitivity analysis
Citation: 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[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 182-213. doi: 10.3934/mbe.2021010

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Abstract

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.

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