How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space
Roberts, M.G., Hickson, R.I., and Mccaw, J.M. (2024) How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space. Journal of Mathematical Biology, 88. 48.
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Abstract
We extend a previously published model for the dynamics of a single strain of an influenza-like infection. The model incorporates a waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of coupled integral equations within a season and a discrete map between seasons. The long term behaviour of the model is demonstrated by examples where immunity to infection depends on the time since a host was last infected, and where immunity depends on the number of times that a host has been infected. The first scenario leads to complicated dynamics in some regions of parameter space, and to regions of parameter space with more than one attractor. The second scenario leads to a stable fixed point, corresponding to an identical epidemic each season. We also examine the model with both paradigms in combination, almost always but not exclusively observing a stable fixed point or periodic solution. Adding stochastic perturbations to the between season map fails to destroy the model’s qualitative dynamics. Our results suggest that if the level of host immunity depends on the elapsed time since the last infection then the epidemiological dynamics may be unpredictable.
| Item ID: | 83171 |
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| Item Type: | Article (Research - C1) |
| ISSN: | 1432-1416 |
| Keywords: | Discrete dynamics, Dynamical systems, Epidemiological modelling, SARS-CoV-2, Seasonal influenza |
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| Copyright Information: | Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Date Deposited: | 17 Jul 2024 23:53 |
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