Discrete-time deterministic and stochastic models for the spread of rabies

  • Authors:

  • Linda J. S. Allen;David A. Flores;Ruwan K. Ratnayake;John R. Herbold

  • Affiliations:

  • Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX;Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX;Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX;School of Public Health, University of Texas, 7703 Floyd Curl Drive, San Antonio, TX

  • Venue:
  • Applied Mathematics and Computation
  • Year:
  • 2002

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Abstract

Discrete spatial and temporal models for the spread and control of rabies are developed, analyzed and simulated. First, a deterministic model is formulated, then an analogous stochastic model. The models are structured with respect to space (m patches), age (juveniles and adults) and disease state. For each patch there are six state variables corresponding to either juveniles or adults and their disease state: susceptible, infected, or vaccinated. The models have seven stages which repeat every year. The impact of different vaccination strategies on the dynamics of the deterministic and stochastic models are compared. In particular, the relationships among the vaccination proportion, the width of the vaccination barrier, the initial number infected, and the transmissibility of the disease are examined. An estimate for the probability of disease elimination is given for the stochastic model. It is shown that in some cases where the deterministic model predicts disease persistence, the stochastic model predicts a high probability of disease elimination.