Incorporating Landscape Heterogeneities in the Spread of an Epidemic in Wildlife (original) (raw)

Modeling spatial spread of communicable diseases involving animal hosts

Chapman & Hall/CRC Mathematical & Computational Biology, 2009

In this chapter, we review some previous studies on modeling spatial spread of specific communicable diseases involving animal hosts. Reaction-diffusion equations are used to model these diseases due to movement of animal hosts. Selected topics include the transmission of rabies in fox populations (

Spatial Spread of Rabies Revisited: Influence of Age‐Dependent Diffusion on Nonlinear Dynamics

SIAM Journal on Applied Mathematics, 2006

We consider the spatio-temporal patterns of disease spread involving structured populations. We start with a general model framework in population biology and spatial ecology where the individual's spatial movement behaviors depend on its maturation status, and we show how delayed reaction diffusion equations with nonlocal interactions arise naturally. We then consider the impact of this delayed nonlocal interaction on the disease spread by revisiting the spatial spread of rabies in continental Europe during the period between 1945 and 1985. We show how the distinction of territorial patterns between juvenile and adult foxes, the main carriers of the rabies under consideration, yields a class of partial differential equations involving delayed and nonlocal terms that are implicitly defined by a hyperbolic-parabolic equation, and we show how incorporating this distinction into the model leads to a formula describing the relation of the minimal wave speed and the maturation time of foxes. We show how the homotopy argument developed by Chow, Lin, and Mallet-Paret can be applied to obtain the existence of a heteroclinic orbit between a disease-free equilibrium and an endemic state for the spatially averaged system of delay differential equations, and we illustrate how the technique developed by Faria, Huang, and Wu can be used to establish the existence of a family of traveling wavefronts in the neighborhood of the heteroclinic orbit for the corresponding spatial model.

Analysis of a rabies transmission model with population dispersal

A two-patch SEIRS epidemic model is proposed to study the impact of travel on the spatial spread of dog rabies between patches with different level of disease prevalence. The basic reproduction number of the system is obtained. It is shown that this number characterizes the disease transmission dynamics: if R 0 < 1, there exists only the disease-free equilibrium which is globally asymptotically stable; and if R 0 > 1 then there is a disease endemic equilibrium and the disease persists. Numerical simulations show that, for the parameter values considered, border restriction does not necessarily always have a positive impact on the overall spread of rabies, only when the border control is properly implemented, then it could contribute to stopping the spatial spread of rabies between patches. We compare the efficiency of three strategies for controlling dog rabies: culling, immunization, culling and immunization. Our studies show that dog rabies in China can be controlled by reducing the birth rate of dogs, increasing the immunization rate of dogs.

Predicting the spatial dynamics of rabies epidemics on heterogeneous landscapes

Proceedings of the National Academy of Sciences, 2002

Often as an epidemic spreads, the leading front is irregular, reflecting spatial variation in local transmission rates. We developed a methodology for quantifying spatial variation in rates of disease spread across heterogeneous landscapes. Based on data for epidemic raccoon rabies in Connecticut, we developed a stochastic spatial model of rabies spread through the state's 169 townships. We quantified spatial variation in transmission rates associated with human demography and key habitat features. We found that large rivers act as semipermeable barriers, leading to a 7-fold reduction in the local rates of propagation. By combining the spatial distribution of major rivers with long-distance dispersal we were able to account for the observed irregular pattern of disease spread across the state without recourse to direct assessment of host-pathogen populations.

Stochastic Modeling and Combined Spatial Pattern Analysis of Epidemic Spreading

We present analysis of spatial patterns of generic disease spread simulated by a stochastic long-range correlation SIR model, where individuals can be infected at long distance in a power law distribution. We integrated various tools, namely perimeter, circularity, fractal dimension, and aggregation index to characterize and investigate spatial pattern formations. Our primary goal was to understand for a given model of interest which tool has an advantage over the other and to what extent. We found that perimeter and circularity give information only for a case of strong correlationwhile the fractal dimension and aggregation index exhibit the growth rule of pattern formation, depending on the degree of the correlation exponent (β). The aggregation index method used as an alternative method to describe the degree of pathogenic ratio (α). This study may provide a useful approach to characterize and analyze the pattern formation of epidemic spreading Keywords-spatial pattern epidemics, aggregation index, fractal dimension, stochastic, long-rang epidemics I. INTRODUCTION ATTERN formation phenomena, occurring via the aggregation process or clustering of particles, has been the subject of increased interest [1]. Spatial pattern analysis plays an important role in many fields of research, ranging from the microscopic to macroscopic scale, including bacteria colonies [2], epidemiology [3], forests, and ecology [4]. Spatial technology enables epidemiologists to create detailed maps and employ spatial cluster statistics to garner insights about patterns of disease [3]. There has been significant development in creating predictive models to better understand the pattern formation of epidemics; see reviews [5-7]. The mathematical epidemiological model usually takes the form of a deterministic model, which consists of a system of ordinary differential equation (ODE) models describing changes in the number of susceptible, infected, and recovered individuals in a given population [8]. Typically, the ODE

S-I-R Epidemic Models with Directed Diffusion

. A generalization of the Gurtin--MacCamy model for an S--I--R epidemic is described. The new model, which includes diffusion away from overcrowded regions, retains many of the interesting qualitative features of previous models. In addition, the global--in--time existence of solutions is proved for a special case. Qualitative properties of the solution are discussed and illustrated with a numerical example. 1. Introduction. Mathematical models for epidemics have been evolving in complexity and realism during the past 60 years. From the simple, unstructured model of Kermack and McKendrick of 1927 [7], many models incorporating, for example, age structure, time delays corresponding to incubation periods, spatial diffusion, and variable infectivity have been proposed (see, e.g., [2], [3], [4], [6]). The effects of dispersion on the spatial distribution of the subpopulations are of primary interest in this work. In addition to allowing for more realistic descriptions of the observed ph...

An S--I--R Model for Epidemics with Diffusion to Avoid Infection and Overcrowding

A model for an epidemic of S--I--R type is described in which susceptibles move to avoid the infection and all individuals move away from overcrowded regions. Some qualitative properties of the mathematical model are discussed. and exhibited with results from numerical simulations. 1 Introduction The Kermack--McKendrick model is the first one to provide a mathematical description for the kinetic transmission of an epidemic in an unstructured population [3]. In this model the total population is assumed to be constant and divided into three classes: susceptible, infected, and removed (or recovered). The propagation of an infection governed by this simple model, which does not incorporate structure due to age, sex, degree of infectivity, or spatial position, is well-known. Several extensions of the model have been considered. Webb [7] proposed and analyzed a model structured by spatial position in a bounded one-dimensional environment, [0; L], L ? 0. The spatial distribution is assume...

Stochastic modeling of animal epidemics using data collected over three different spatial scales

Epidemics, 2011

A stochastic, spatial, discrete-time, SEIR model of avian influenza epidemics among poultry farms in Pennsylvania is formulated. Using three different spatial scales wherein all the birds within a single farm, ZIP code, or county are clustered into a single point, we obtain three different views of the epidemics. For each spatial scale, two parameters within the viral-transmission kernel of the model are estimated using simulated epidemic data. We show that simulated epidemics modeled using data collected on the farm and ZIP-code levels behave similar to the actual underlying epidemics, but this is not true using data collected on the county level. Such analyses of data collected on different spatial scales are useful in formulating intervention strategies to control an ongoing epidemic (e.g., vaccination schedules and culling policies).