Optimal control and stability analysis of an age-structured SEIRV model with imperfect vaccination

Manoj Kumar, Syed Abbas, Abdessamad Tridane

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Vaccination programs are crucial for reducing the prevalence of infectious diseases and ultimately eradicating them. A new age-structured SEIRV (S-Susceptible, E-Exposed, I-Infected, R-Recovered, V-Vaccinated) model with imperfect vaccination is proposed. After formulating our model, we show the existence and uniqueness of the solution using semigroup of operators. For stability analysis, we obtain a threshold parameter R0. Through rigorous analysis, we show that if R0 < 1, then the disease-free equilibrium point is stable. The optimal control strategy is also discussed, with the vaccination rate as the control variable. We derive the optimality conditions, and the form of the optimal control is obtained using the adjoint system and sensitivity equations. We also prove the uniqueness of the optimal controller. To visually illustrate our theoretical results, we also solve the model numerically.

Original languageEnglish
Pages (from-to)14438-14463
Number of pages26
JournalMathematical Biosciences and Engineering
Issue number8
Publication statusPublished - 2023


  • age-structured model
  • imperfect vaccination
  • optimal control

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Agricultural and Biological Sciences
  • Computational Mathematics
  • Applied Mathematics


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