Disease outbreaks in plant-vector-virus models with vector aggregation and dispersal

Mary P.  Hebert; Linda J. S. Allen

doi:10.3934/dcdsb.2016042

Article Contents

2016, Volume 21, Issue 7: 2169-2191. Doi: 10.3934/dcdsb.2016042

This issue Previous Article Stochastic models in biology and the invariance problem Next Article Ergodicity and loss of capacity for a random family of concave maps

Disease outbreaks in plant-vector-virus models with vector aggregation and dispersal

Mary P. Hebert^1, and
Linda J. S. Allen^2,

1.
Department of Mathematics, Lower Columbia College, Longview, WA 98632
2.
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042

Received: May 31, 2015

Revised: March 31, 2016

Published: August 2016

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Abstract

While feeding on host plants, viruliferous insects serve as vectors for viruses. Successful viral transmission depends on vector behavior. Two behaviors that impact viral transmission are vector aggregation and dispersal. Vector aggregation may be due to chemical or visual cues or feeding preferences. Vector dispersal can result in widespread disease outbreaks among susceptible host plants. These two behaviors are investigated in plant-vector-virus models. Deterministic and stochastic models are formulated to account for stages of infection, vector aggregation and local dispersal between adjacent crops. First, models for a single crop are studied with aggregation included implicitly through the acquisition and inoculation rates. Second, models with aggregation and dispersal of vectors are studied when one field contains a disease-sensitive crop and another a disease-resistant crop. Analytical expressions are computed for the basic reproduction number in the deterministic models and for the probability of disease extinction in the stochastic models. These two expressions provide useful measures to assess effects of aggregation and dispersal on the rate of disease spread within and between crops and the potential for an outbreak. The modeling framework is based on cassava mosaic virus that causes significant damage in cassava crops in Africa.

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Mathematics Subject Classification: Primary: 92D30, 60J28; Secondary: 34D23.

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