Work

Threshold dynamics of a seasonally forced stochastic chikungunya host–vector model with extrinsic incubation and Lévy jumps

Year: 2026

Type: article

Abstract: This paper is concerned with a seasonally forced stochastic model of chikungunya transmission between a human host and an Aedes vector. The human population is divided into susceptible, infectious and recovered classes, and the mosquito population into susceptible, exposed and infectious classes, the exposed class representing the extrinsic incubation period explicitly. The biting rate, the transmission probabilities, the vector recruitment and mortality rates and the incubation rate are positive, continuous and periodic in time For the deterministic model the disease-free state is a periodic orbit, the reproduction number ℛ 0 is the spectral radius of a seasonal next-generation operator, and a seasonal incubation survival kernel describes how the timing of exposure affects the contribution of each infected mosquito. The system is then perturbed by multiplicative Brownian noise and compensated Lévy jumps in every compartment. We prove global existence, uniqueness and positivity of solutions, and we introduce a noise-corrected seasonal threshold ℛ 𝛥 0 on the generation scale which reduces to the averaged deterministic threshold when the noise vanishes. An extinction criterion is derived using periodic Lyapunov weights constructed from the principal Floquet eigenfunction, so that its deterministic part coincides with the exact Floquet exponent; persistence in the mean is established when ℛ 𝛥 0 > 1 . By adjoining the seasonal phase, we construct an explicit Lyapunov function and a minorisation set for the period map and prove that the periodic endemic regime is unique and exponentially attracting. All constants are computed for parameter sets that satisfy the hypotheses, and simulations illustrate classical extinction, noise-induced extinction from a supercritical seasonal regime, and a persistent noisy periodic endemic regime, together with a quantitative convergence diagnostic.

Source: Results in Control and Optimization

DOI: 10.1016/j.rico.2026.100877

Authors: Umar Ishtiaq, Mehran, Tayyab Kamran, Ioan-Lucian Popa

Institutions: University of Management and Technology, Quaid-i-Azam University, Transilvania University of Brașov, 1 Decembrie 1918 University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $1,470