The Impact of Imperfect Vaccination on Infectious Disease Transmission in an Age-Structured Population
Abstract
In this paper, we consider the influence of imperfect vaccination on the spread of infectious diseases in an age-structured population. The benefits of vaccination, even if not perfect, generally outweigh the risks of severe diseases. In a mathematical system, we consider the compartment of susceptible s; vaccinated v and infected i individuals with an age structure. The proposed model is globally analyzed by introducing total trajectories and employing a suitable Lyapunov functional. To illustrate our theoretical findings, we include numerical simulations at the end of the paper.
AMS subject classification: 35Q92, 37N25, 92D30.
REFERENCES
[1] Adimy, M., Chekroun, A., & Ferreira, C. P. (2020). Global dynamics of a differential-difference system: a case of Kermack-McKendrick SIR model with age-structured protection phase. Mathematical Biosciences and Engineering, 17(2), 1329-1354. Search in Google Scholar. https://dx.doi.org/10.3934/mbe.2020067
[2] Benchaira, S., Mancer, S., & Necir, A. (2024). A Log-Probability-Weighted-Moments type estimator for the extreme value index in a truncation scheme. International Journal of Applied Mathematics and Simulation, 1(2). Search in Google Scholar. https://doi.org/10.69717/ijams.v1.i2.99
[3] Soufiane, B., & Touaoula, T. M. (2016). Global analysis of an infection age model with a class of nonlinear incidence rates. Journal of Mathematical Analysis and Applications, 434(2), 1211-1239. Search in Google Scholar.…
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