article · Chaos Solitons & Fractals
This research examines epidemic modelling for COVID-19 under unpredictable environmental conditions. The study establishes a stochastic SIQS epidemic model, which features a specific compartment for quarantined populations, to capture the behavioural dynamics of the virus amid external fluctuations. By incorporating both white noise and Lévy jump noise, the framework accounts for inherent randomness and sudden disruptions in the transmission process. Analysis reveals that the long-term behaviour of the epidemic is governed by two defined mathematical thresholds. When the lower threshold is below one, the disease eventually disappears from the population, whereas exceeding the upper threshold leads to disease persistence. In the absence of jump perturbations, the analysis establishes necessary and sufficient conditions for disease extinction, making the conditions for the jump scenario nearly necessary as well. Computational simulations confirm these theoretical thresholds.
Real-world disease outbreaks are subject to sudden shifts, unpredictable public behaviour, and environmental fluctuations. By accounting for random disruptions and quarantine dynamics, this mathematical approach helps demystify how viral transmission behaves under real-world volatility. Understanding precise mathematical conditions for disease extinction versus persistence provides valuable insights for evaluating how quarantine measures and unpredictable events influence the course of an epidemic.
The abstract does not indicate an application pathway or a direct commercial deployment. The work is theoretical and computational early-stage research that provides mathematical formulations and simulations of epidemic dynamics, which could primarily inform future analytical tools or academic software for disease modelling rather than offering an immediate market product.
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This work delves into the intricate realm of epidemic modeling under the influence of unpredictable surroundings. By harnessing the power of white noise and Lévy noise, we construct a robust framework to capture the behavioral characteristics of the COVID-19 epidemic amidst erratic changes in the external environment. To enhance our comprehension of the intricate dynamics of the coronavirus, we conducted an investigation using a stochastic SIQS epidemic model that incorporates a dedicated compartment to represent populations under quarantine. Thanks to stochastic modeling techniques, we account for the inherent randomness in the transmission process and provide insights into the potential variations and uncertainties associated with the progression of the epidemic. Specifically, we show that the asymptotic behavior of our model is perfectly governed by two thresholds, Rσ,J and Rσ,J′. That is to say, if Rσ,J<1, the disease will be removed from the population, while it will persist if Rσ,J′>1. Our highlight lies in obtaining the necessary and sufficient conditions for extinction in the absence of jump noise, namely Rσ,0=Rσ,0′. This means that our sufficient conditions for extinction for the jump case are also almost necessary. Finally, we present a set of computational simulations to validate our theoretical findings, supporting the results developed throughout this article. Overall, this research contributes to our understanding of the COVID-19 pandemic and its impact on the global population.
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DOI: 10.1016/j.chaos.2024.114521
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