Gai, C and Kolokolnikov, T and Schrader, J and Sharma, V (2024) Recurrent and chaotic outbreaks in SIR model. In: European Journal of Applied Mathematics .
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Abstract
We examine several extensions to the basic Susceptible-Infected-Recovered model, which are able to induce recurrent outbreaks (the basic Susceptible-Infected-Recovered model by itself does not exhibit recurrent outbreaks). We first analyse how slow seasonal variations can destabilise the endemic equilibrium, leading to recurrent outbreaks. In the limit of slow immunity loss, we derive asymptotic thresholds that characterise this transition. In the outbreak regime, we use asymptotic matching to obtain a two-dimensional discrete map which describes outbreak times and strength. We then analyse the resulting map using linear stability and numerics. As the frequency of forcing is increased, the map exhibits a period-doubling route to chaos which alternates with periodic outbreaks of increasing frequency. Other extensions that can lead to recurrent outbreaks include the addition of noise, state-dependent variation and fine-graining of model classes. © The Author(s), 2024. Published by Cambridge University Press.
| Item Type: | Journal Article |
|---|---|
| Publication: | European Journal of Applied Mathematics |
| Publisher: | Cambridge University Press |
| Additional Information: | The copyright for this article belongs to Author. |
| Keywords: | Asymptotics; Chaotics; Discrete map, period doubling; Discrete maps; Endemic equilibrium; Period-doubling; Recurrent outbreak; Seasonal variation; SIR model; Susceptible-infected-recovered model |
| Department/Centre: | Others |
| Date Deposited: | 01 Mar 2024 09:00 |
| Last Modified: | 01 Mar 2024 09:00 |
| URI: | https://eprints.iisc.ac.in/id/eprint/83942 |
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