# Numerical simulations of spread of rabies in a spatially distributed fox population

Khalaf M. Alanazi, Zdzislaw Jackiewicz, Horst Thieme

Research output: Contribution to journalArticle

### Abstract

We describe a numerical algorithm for the simulation of the spread of rabies in a spatially distributed fox population. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. The resulting systems are mixtures of partial differential and integral equations. They are discretized in the space variable by central differences of second order and by the composite trapezoidal rule. In a second step, they are discretized in time by explicit continuous Runge–Kutta methods of fourth order for ordinary and delay differential systems. The results of the numerical calculations are compared for latent periods of fixed and exponentially distributed length and for various proportions of territorial and wandering rabid foxes. The speeds of spread observed in the simulations are compared to spreading speeds obtained by analytic methods and to observed speeds of epizootic frontlines in the European rabies outbreak 1940 to 1980.

Original language English (US) Mathematics and Computers in Simulation https://doi.org/10.1016/j.matcom.2018.11.010 Accepted/In press - Jan 1 2018

### Fingerprint

Delay-differential Systems
Numerical Simulation
Trapezoidal Rule
Computer simulation
Runge-Kutta Methods
Numerical Algorithms
Numerical Calculation
Fourth Order
Infection
Integral Equations
Simulation
Proportion
Partial differential equation
Composite
Partial differential equations
Integral equations
Composite materials
Model

### Keywords

• Continuous Runge–Kutta method
• Diffusing versus territorial rabid foxes
• Latent period
• Method of lines

### ASJC Scopus subject areas

• Theoretical Computer Science
• Computer Science(all)
• Numerical Analysis
• Modeling and Simulation
• Applied Mathematics

### Cite this

In: Mathematics and Computers in Simulation, 01.01.2018.

Research output: Contribution to journalArticle

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AB - We describe a numerical algorithm for the simulation of the spread of rabies in a spatially distributed fox population. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. The resulting systems are mixtures of partial differential and integral equations. They are discretized in the space variable by central differences of second order and by the composite trapezoidal rule. In a second step, they are discretized in time by explicit continuous Runge–Kutta methods of fourth order for ordinary and delay differential systems. The results of the numerical calculations are compared for latent periods of fixed and exponentially distributed length and for various proportions of territorial and wandering rabid foxes. The speeds of spread observed in the simulations are compared to spreading speeds obtained by analytic methods and to observed speeds of epizootic frontlines in the European rabies outbreak 1940 to 1980.

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