Rich dynamics of a partially degenerate reaction-advection-diffusion mosquito-borne disease model with multiple transmission routes, latent periods and human behavior change

The spatiotemporal dynamics of mosquito-borne diseases are driven by host movement, vector dispersal, and environmental heterogeneity, while human behavioral responses often considerably modulate intervention effectiveness. To quantitatively capture these factors, we propose a degenerated reaction-advection-diffusion model that unifies multi-route host infections, host-vector transmission, and individual movement, with host psychological factors embedded as an endogenous component of control, yielding a framework more reflective of realistic epidemic settings. A generalized incidence describes direct contact, enhancing model adaptability. By refined estimates and inductive method, we establish the well-posedness of solutions and the existence of a global attractor. Following next-generation operator, the definition of basic reproduction number\, (BRN) $ \mathscr{R}_{0} $ is given, along with its explicit expression. Threshold analysis shows that for $ \mathscr{R}_{0}< 1 $, the disease-free steady state\, (DFSS)\, is globally asymptotically stable\, (GAS); for $ \mathscr{R}_{0}> 1 $, the disease becomes endemic and the model has at least one positive steady state\, (PSS). In particular, in a spatially homogeneous environment without advection, this PSS is globally attractive. Furthermore, with no advection, we derive the GAS of DFSS when $ \mathscr{R}_{0} = 1 $, as well as the asymptotic profiles of PSS as susceptible diffusion rates tend to 0 or infinity. Numerical simulations indicate that a higher advection coefficient greatly reduces the early-stage epidemic size, while human behavior effectively lowers the outbreak peak, especially in high-risk areas during the early phase. Finally, using the Markov chain Monte Carlo\, (MCMC) method, the model successfully fits Zika virus data from Brazil, demonstrating its potential for practical application.

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Publication Details

Journal
Communications on Pure &amp Applied Analysis
Published
2026-10-26
DOI
https://doi.org/10.3934/cpaa.2026.102937
Primary Topic
Mathematical and Theoretical Epidemiology and Ecology Models
Type
article
Field-Weighted Citation Impact
0.00

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article

Rich dynamics of a partially degenerate reaction-advection-diffusion mosquito-borne disease model with multiple transmission routes, latent periods and human behavior change

Linfei Nie, Yingchao Yu
Communications on Pure &amp Applied Analysis
Mathematical and Theoretical Epidemiology and Ecology Models
article

Rich dynamics of a partially degenerate reaction-advection-diffusion mosquito-borne disease model with multiple transmission routes, latent periods and human behavior change

Linfei Nie, Yingchao Yu
article en

Abstract

The spatiotemporal dynamics of mosquito-borne diseases are driven by host movement, vector dispersal, and environmental heterogeneity, while human behavioral responses often considerably modulate intervention effectiveness. To quantitatively capture these factors, we propose a degenerated reaction-advection-diffusion model that unifies multi-route host infections, host-vector transmission, and individual movement, with host psychological factors embedded as an endogenous component of control, yielding a framework more reflective of realistic epidemic settings. A generalized incidence describes direct contact, enhancing model adaptability. By refined estimates and inductive method, we establish the well-posedness of solutions and the existence of a global attractor. Following next-generation operator, the definition of basic reproduction number\, (BRN) $ \mathscr{R}_{0} $ is given, along with its explicit expression. Threshold analysis shows that for $ \mathscr{R}_{0}< 1 $, the disease-free steady state\, (DFSS)\, is globally asymptotically stable\, (GAS); for $ \mathscr{R}_{0}> 1 $, the disease becomes endemic and the model has at least one positive steady state\, (PSS). In particular, in a spatially homogeneous environment without advection, this PSS is globally attractive. Furthermore, with no advection, we derive the GAS of DFSS when $ \mathscr{R}_{0} = 1 $, as well as the asymptotic profiles of PSS as susceptible diffusion rates tend to 0 or infinity. Numerical simulations indicate that a higher advection coefficient greatly reduces the early-stage epidemic size, while human behavior effectively lowers the outbreak peak, especially in high-risk areas during the early phase. Finally, using the Markov chain Monte Carlo\, (MCMC) method, the model successfully fits Zika virus data from Brazil, demonstrating its potential for practical application.

Communications on Pure &amp Applied AnalysisVol. 40(0)
Xinjiang University (CN)
National Natural Science Foundation of China, Natural Science Foundation of Xinjiang
Openalex Percentile: Top 10%
Mathematical and Theoretical Epidemiology and Ecology Models
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