TY - JOUR
T1 - Optimal control and stability analysis of an age-structured SEIRV model with imperfect vaccination
AU - Kumar, Manoj
AU - Abbas, Syed
AU - Tridane, Abdessamad
N1 - Funding Information:
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions that helped improve this manuscript’s quality. A. Tridane is supported by UAEU UPAR grant number 12S125.
Publisher Copyright:
© 2023 the Author(s)
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - age-structured model
KW - imperfect vaccination
KW - optimal control
UR - http://www.scopus.com/inward/record.url?scp=85165220184&partnerID=8YFLogxK
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U2 - 10.3934/mbe.2023646
DO - 10.3934/mbe.2023646
M3 - Article
C2 - 37679143
AN - SCOPUS:85165220184
SN - 1547-1063
VL - 20
SP - 14438
EP - 14463
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
IS - 8
ER -
