Analysis of a diffusive host-pathogen model with standard incidence and distinct dispersal rates

Abstract

This paper concerns with detailed analysis of a reaction-diffusion host-pathogen model with space-dependent parameters in a bounded domain. By considering the fact the mobility of host individuals playing a crucial role in disease transmission, we formulate the model by a system of degenerate reaction-diffusion equations, where host individuals disperse at distinct rates and the mobility of pathogen is ignored in the environment.We first establish the well-posedness of the model, including the global existence of solution and the existence of the global compact attractor. The basic reproduction number is identified, and also characterized by some equivalent principal spectral conditions, which establishes the threshold dynamical result for pathogen extinction and persistence. When the positive steady state is confirmed, we investigate the asymptotic profiles of positive steady state as host individuals disperse at small and large rates. Our result suggests that small and large diffusion rate of hosts have a great impacts in formulating the spatial distribution of the pathogen.

Analysis on a diffusive SEI epidemic model with/without immigration of infected hosts

“…To understand how small immigration rate of the susceptible, infected or exposed population affects the spatial distribution of the disease modelled by ( 2) and ( 5), as in [6,22,32,36,47,51,55,56], we have studied the asymptotic behavior of the EE (when it exists) as the immigration rate d S , d I or d E tends to zero. To guarantee the existence of EE for (4) with respect to small d S , d I or d E , we are led to determine the limits of the the basic reproduction number R 0 ; see Proposition 2.…”

“…Clearly, by (47), λ n = 0 for all n ≥ 1 as (E n , I n ) is a corresponding eigenfunction. By Proposition 2 (ii), we can see R n 0 → 1 1 as d E → 0, where 1 is the principal eigenvalue of (19).…”

Dynamics of a partially degenerate reaction-diffusion cholera model with horizontal transmission and phage-bacteria interaction

“…Note that the above mentioned models are discussed in a homogeneous space. However, differences in spatial location, water availability and sanitation have a important impact on the transmission of diseases, so it is necessary to consider reaction-diffusion models with spatial heterogeneity [48,51,52,54].…”

Threshold Dynamics of a Diffusive Herpes Model Incorporating Fixed Relapse Period in a Spatial Heterogeneous Environment

“…e spatial heterogeneity (SH) and diffusion play important roles in disease transmission. Under different infection mechanisms, some new insights in disease control and new phenomenon in disease spread will be obtained; see, for instance, [8][9][10][11][12][13]. It is found in [8] that SH would increase the risk of influenza transmission so that the SH of the recovery rate and transmission rate must be increased for controlling the influenza transmission.…”