Modeling mosquito-borne disease dynamics via stochastic differential equations and generalized tempered stable distribution

Yassine Sabbar; Aeshah A. Raezah; Yassine Sabbar; Aeshah A. Raezah

doi:10.3934/math.20241092

AIMS Mathematics

2024, Volume 9, Issue 8: 22454-22485. doi: 10.3934/math.20241092

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Modeling mosquito-borne disease dynamics via stochastic differential equations and generalized tempered stable distribution

Yassine Sabbar ^{1
,
,},
Aeshah A. Raezah ²

1.
MAIS Laboratory, MAMCS Group, FST Errachidia, Moulay Ismail University of Meknes, P.O. Box 509, Errachidia 52000, Morocco
2.
Department of Mathematics, Faculty of Science King Khalid, University Abha, 62529, Saudi Arabia

Received: 06 May 2024 Revised: 05 July 2024 Accepted: 15 July 2024 Published: 18 July 2024
MSC : 37A50

In this study, we introduce an enhanced stochastic model for mosquito-borne diseases that incorporates quarantine measures and employs Lévy jumps with the generalized tempered stable (GTS) distribution. Our proposed model lacks both endemic and disease-free states, rendering the conventional approach of assessing disease persistence or extinction based on asymptotic behavior inapplicable. Instead, we adopt a novel stochastic analysis approach to demonstrate the potential for disease eradication or continuation. Numerical examples validate the accuracy of our results and compare the outcomes of our model with the GTS distribution against the standard system using basic Lévy jumps. By accounting for the heavy-tailed nature of disease incidence or vector abundance, the GTS distribution enhances the precision of epidemiological models and predictions.
- epidemic model,
- mosquito-borne disease,
- GTS distribution,
- Lévy jumps,
- Lévy measure
Citation: Yassine Sabbar, Aeshah A. Raezah. Modeling mosquito-borne disease dynamics via stochastic differential equations and generalized tempered stable distribution[J]. AIMS Mathematics, 2024, 9(8): 22454-22485. doi: 10.3934/math.20241092

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Abstract

In this study, we introduce an enhanced stochastic model for mosquito-borne diseases that incorporates quarantine measures and employs Lévy jumps with the generalized tempered stable (GTS) distribution. Our proposed model lacks both endemic and disease-free states, rendering the conventional approach of assessing disease persistence or extinction based on asymptotic behavior inapplicable. Instead, we adopt a novel stochastic analysis approach to demonstrate the potential for disease eradication or continuation. Numerical examples validate the accuracy of our results and compare the outcomes of our model with the GTS distribution against the standard system using basic Lévy jumps. By accounting for the heavy-tailed nature of disease incidence or vector abundance, the GTS distribution enhances the precision of epidemiological models and predictions.

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