An immuno-epidemiological model with waning immunity after infection or vaccination
Angelov G, Kovacevic R, Stilianakis NI, Veliov VM (2024)
Publication Type: Journal article
Publication year: 2024
Journal
Book Volume: 88
Article Number: 71
Journal Issue: 6
DOI: 10.1007/s00285-024-02090-z
Abstract
In epidemics, waning immunity is common after infection or vaccination of individuals. Immunity levels are highly heterogeneous and dynamic. This work presents an immuno-epidemiological model that captures the fundamental dynamic features of immunity acquisition and wane after infection or vaccination and analyzes mathematically its dynamical properties. The model consists of a system of first order partial differential equations, involving nonlinear integral terms and different transfer velocities. Structurally, the equation may be interpreted as a Fokker-Planck equation for a piecewise deterministic process. However, unlike the usual models, our equation involves nonlocal effects, representing the infectivity of the whole environment. This, together with the presence of different transfer velocities, makes the proved existence of a solution novel and nontrivial. In addition, the asymptotic behavior of the model is analyzed based on the obtained qualitative properties of the solution. An optimal control problem with objective function including the total number of deaths and costs of vaccination is explored. Numerical results describe the dynamic relationship between contact rates and optimal solutions. The approach can contribute to the understanding of the dynamics of immune responses at population level and may guide public health policies.
Involved external institutions
Universität für Weiterbildung / Donau-Universität Krems
Austria (AT)
Technische Universität Wien / Vienna University of Technology
Austria (AT)
European Commission - Joint Research Centre (JRC)
Netherlands (NL)
Austria (AT)
Technische Universität Wien / Vienna University of Technology
Austria (AT)
European Commission - Joint Research Centre (JRC)
Netherlands (NL)
How to cite
APA:
Angelov, G., Kovacevic, R., Stilianakis, N.I., & Veliov, V.M. (2024). An immuno-epidemiological model with waning immunity after infection or vaccination. Journal of Mathematical Biology, 88(6). https://doi.org/10.1007/s00285-024-02090-z
MLA:
Angelov, Georgi, et al. "An immuno-epidemiological model with waning immunity after infection or vaccination." Journal of Mathematical Biology 88.6 (2024).
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