Impact of immunity loss on the optimal vaccination strategy for an age-structured epidemiological model

Amira Bouhali; Walid Ben Aribi; Slimane Ben Miled; Amira Kebir; Amira Bouhali; Walid Ben Aribi; Slimane Ben Miled; Amira Kebir

doi:10.3934/mbe.2024278

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 6: 6372-6392. doi: 10.3934/mbe.2024278

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Impact of immunity loss on the optimal vaccination strategy for an age-structured epidemiological model

1.
BioInformatics, bioMathematics and bioStatistics (BIMS-LR16IPT09), Institute Pasteur of Tunis, University of Tunis El Manar, Tunis 1002, Tunisia
2.
National Engineering School of Tunis, University of Tunis El Manar, Tunis 1002, Tunisia
3.
School of Business, Esprit School of Business, Ariana 2083, Tunisia
4.
Preparatory Institute for Engineering Studies in Tunis, Tunis University, Tunis 1089, Tunisia

Received: 02 January 2024 Revised: 23 March 2024 Accepted: 10 May 2024 Published: 26 June 2024

The pursuit of effective vaccination strategies against COVID-19 remains a critical endeavour in global public health, particularly amidst challenges posed by immunity loss and evolving epidemiological dynamics. This study investigated optimal vaccination strategies by considering age structure, immunity dynamics, and varying maximal vaccination rates. To this end, we formulated an SEIR model stratified into $ n $ age classes, with the vaccination rate as an age-dependent control variable in an optimal control problem. We developed an objective function aimed at minimising critical infections while optimising vaccination efforts and then conducted rigorous mathematical analyses to ensure the existence and characterization of the optimal control. Using data from three countries with diverse age distributions, in expansive, constrictive, and stationary pyramids, we performed numerical simulations to evaluate the optimal age-dependent vaccination strategy, number of critical infections, and vaccination frequency. Our findings highlight the significant influence of maximal vaccination rates on shaping optimal vaccination strategies. Under constant maximal vaccination rates, prioritising age groups based on population demographics proves effective, with higher rates resulting in fewer critically infected individuals across all age distributions. Conversely, adopting age-dependent maximal vaccination rates, akin to the WHO strategy, may not always lead to the lowest critical infection peaks but offers a viable alternative in resource-constrained settings.
- optimal control,
- epidemiology,
- long-term vaccination,
- COVID-19,
- age-structured model
Citation: Amira Bouhali, Walid Ben Aribi, Slimane Ben Miled, Amira Kebir. Impact of immunity loss on the optimal vaccination strategy for an age-structured epidemiological model[J]. Mathematical Biosciences and Engineering, 2024, 21(6): 6372-6392. doi: 10.3934/mbe.2024278

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Abstract

The pursuit of effective vaccination strategies against COVID-19 remains a critical endeavour in global public health, particularly amidst challenges posed by immunity loss and evolving epidemiological dynamics. This study investigated optimal vaccination strategies by considering age structure, immunity dynamics, and varying maximal vaccination rates. To this end, we formulated an SEIR model stratified into $ n $ age classes, with the vaccination rate as an age-dependent control variable in an optimal control problem. We developed an objective function aimed at minimising critical infections while optimising vaccination efforts and then conducted rigorous mathematical analyses to ensure the existence and characterization of the optimal control. Using data from three countries with diverse age distributions, in expansive, constrictive, and stationary pyramids, we performed numerical simulations to evaluate the optimal age-dependent vaccination strategy, number of critical infections, and vaccination frequency. Our findings highlight the significant influence of maximal vaccination rates on shaping optimal vaccination strategies. Under constant maximal vaccination rates, prioritising age groups based on population demographics proves effective, with higher rates resulting in fewer critically infected individuals across all age distributions. Conversely, adopting age-dependent maximal vaccination rates, akin to the WHO strategy, may not always lead to the lowest critical infection peaks but offers a viable alternative in resource-constrained settings.

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