Stochastic spatial models of plant diseases
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arXiv
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| Format: | Preprint |
| Published: |
2001
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| _version_ | 1866914099342868480 |
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| author | Brown, David H. |
| author_facet | Brown, David H. |
| contents | I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of timescales argument to determine the effects of spatial clustering on threshold structure. By computing the spatial structure early in an invasion, I find explicit corrections to mean field theory. In the first chapter, I present a lattice model of a disease that is not directly lethal to its host, but affects its ability to compete with neighbors. I use a type of pair approximation to determine conditions for invasions and coexistence. In the second chapter, I study a basic SIR epidemic point process in continuous space. I implement a multiplicative moment closure scheme to compute the threshold transmission rate as a function of spatial parameters. In the final chapter, I model the evolution of pathogen resistance when two plant species share a pathogen. Evolution may lead to non--resistance by a host that finds the disease to be a useful weapon. I use a lattice model with the ordinary pair approximation assumption to study phenotypic evolution via repeated invasions by novel strains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0112094 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | Stochastic spatial models of plant diseases Brown, David H. Numerical Analysis Probability Quantitative Biology 92D40 (Primary) 60K35 (Secondary) I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of timescales argument to determine the effects of spatial clustering on threshold structure. By computing the spatial structure early in an invasion, I find explicit corrections to mean field theory. In the first chapter, I present a lattice model of a disease that is not directly lethal to its host, but affects its ability to compete with neighbors. I use a type of pair approximation to determine conditions for invasions and coexistence. In the second chapter, I study a basic SIR epidemic point process in continuous space. I implement a multiplicative moment closure scheme to compute the threshold transmission rate as a function of spatial parameters. In the final chapter, I model the evolution of pathogen resistance when two plant species share a pathogen. Evolution may lead to non--resistance by a host that finds the disease to be a useful weapon. I use a lattice model with the ordinary pair approximation assumption to study phenotypic evolution via repeated invasions by novel strains. |
| title | Stochastic spatial models of plant diseases |
| topic | Numerical Analysis Probability Quantitative Biology 92D40 (Primary) 60K35 (Secondary) |
| url | https://arxiv.org/abs/math/0112094 |