Dynamics of a Lyme disease model with environmental and stage-structured vector effects
Abstract
In this paper, we develop a periodic degenerate reaction-diffusion model of Lyme disease with seasonal and spatially heterogeneous structure in both host and tick populations. Moreover, the tick population is divided into three stages: larva, nymph and adult, each exhibiting distinct feeding preferences for two vertebrate hosts. We introduce the basic reproduction ratio R0 for this model and establish that the disease-free periodic solution is globally asymptotically stable if R01. Numerically, we investigate the spread of Lyme disease in Bulgaria. Simulations support our analytical findings and highlight the important role that environmental heterogeneity plays in the transmission dynamics of Lyme disease.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Vector-borne infectious diseases
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Applicable Analysis
- Volume
- 105
- Issue
- 10
- Pages
- 2252–2280
- Publication date
- 13 January 2026
- Language
- EN