A simple model for the spatial spread and control of rabies

Small World Effect in an Epidemiological Model

“…A second classical approach describes spatially extended subpopulations. In this, the geographic spread of an epidemic can be analyzed as a reaction-diffusion process [10][11][12].…”

Seasonal Forcing Drives Spatio-Temporal Pattern Formation in Rabies Epidemics

“…[1,15,16,25]. Despite differences in details all of these models are variants of spatial SIR models.…”

“…The spreading of rabies in Europe is characterized by the appearance of epidemic wave fronts. A peculiar feature is that, behind the first wave of infections in a new area, subsequent smaller waves follow [1,15,12,16].…”

Spatial-Temporal Dynamics in Nonlocal Epidemiological Models

“…De Mottoni et al (1979) and Busenberg and Travis (1983) considered a population in an open bounded region and assumed that the susceptible, infective, and removed individuals can migrate inside the region according to the rules of group migration. The existence of traveling waves in epidemic models described by reaction-diffusion systems has been extensively studied by many researchers, for example, Thieme (1980), Källen et al (1985), Murray et al (1986) and Murray and Seward (1992) In this article we try to provide a short survey on the spatial-temporal dynamics of nonlocal epidemiological models, include the classical KermackMcKendrick model, the Kendall model given by differential and integral equations, the Diekmann-Thieme model described by a double integral equation, the diffusive integral equations proposed by De Mottoni et al (1979) and Busenberg and Travis (1983), a vector-disease model described by a diffusive double integral equation (Ruan and Xiao 2004), etc. Kermack and McKendrick (1927) proposed a simple deterministic model of a directly transmitted viral or bacterial agent in a closed population based on the following assumptions: (i) a single infection triggers an autonomous process within the host; (ii) the disease results in either complete immunity or death; (iii) contacts are according to the law of mass-action; (iv) all individuals are equally susceptible; (v) the population is closed in the sense that at the time-scale of disease transmission the inflow of new susceptibles into the population is negligible; (vi) the population size is large enough to warrant a deterministic description.…”