Mathematical model of COVID-19 with comorbidity and controlling using non-pharmaceutical interventions and vaccination

Parthasakha Das, Ranjit Kumar Upadhyay, Arvind Kumar Misra, Fathalla A. Rihan, Pritha Das, Dibakar Ghosh

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


Pandemic is an unprecedented public health situation, especially for human beings with comorbidity. Vaccination and non-pharmaceutical interventions only remain extensive measures carrying a significant socioeconomic impact to defeating pandemic. Here, we formulate a mathematical model with comorbidity to study the transmission dynamics as well as an optimal control-based framework to diminish COVID-19. This encompasses modeling the dynamics of invaded population, parameter estimation of the model, study of qualitative dynamics, and optimal control problem for non-pharmaceutical interventions (NPIs) and vaccination events such that the cost of the combined measure is minimized. The investigation reveals that disease persists with the increase in exposed individuals having comorbidity in society. The extensive computational efforts show that mean fluctuations in the force of infection increase with corresponding entropy. This is a piece of evidence that the outbreak has reached a significant portion of the population. However, optimal control strategies with combined measures provide an assurance of effectively protecting our population from COVID-19 by minimizing social and economic costs.

Original languageEnglish
Pages (from-to)1213-1227
Number of pages15
JournalNonlinear Dynamics
Issue number2
Publication statusPublished - Oct 2021


  • COVID-19
  • Comorbidity
  • Forward bifurcation
  • Optimal control
  • Shannon entropy

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics


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