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

• Published in: Mathematical biosciences and engineering : MBE Vol. 21; no. 6; pp. 6372 - 6392
• Main Authors: Bouhali, Amira, Aribi, Walid Ben, Miled, Slimane Ben, Kebir, Amira
• Format: Journal Article
• Language: English
• Published: United States 26.06.2024
• Subjects: Adolescent; Adult; Age Factors; Aged; Child; Computer Simulation; COVID-19 - epidemiology; COVID-19 - prevention & control; COVID-19 Vaccines - administration & dosage; Epidemiological Models; Humans; Immunity; Middle Aged; Pandemics - prevention & control; SARS-CoV-2 - immunology; Vaccination; Young Adult; COVID-19; epidemiology; optimal control; age-structured model; long-term vaccination
• ISSN: 1551-0018; 1551-0018
• DOI: 10.3934/mbe.2024278

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.