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Bayesian analysis of botanical epidemics using stochastic compartmental models.
G J Gibson1, A Kleczkowski, C A Gilligan
1Department of Actuarial Mathematics and Statistics, Heriot Watt University, Riccarton, Edinburgh EH14 4AS, United Kingdom. g.j.gibson@ma.hw.ac.uk
Summary
This study introduces a new stochastic epidemic model to estimate infection rates and latent periods. The Bayesian approach accurately models disease spread, even with limited data, and confirms biological control effectiveness.
Area of Science:
- Epidemiology
- Mathematical Biology
- Mycology
Background:
- Epidemic modeling is crucial for understanding disease dynamics.
- Stochastic models offer a robust framework for epidemiological analysis.
- Biological control agents can influence pathogen transmission.
Purpose of the Study:
- To develop a stochastic epidemic model incorporating susceptible, latent, and infectious states.
- To apply a Bayesian framework using Markov chain Monte Carlo (MCMC) for model fitting.
- To investigate the impact of biological control on primary and secondary infections.
Main Methods:
- Developed a stochastic compartmental model (Susceptible-Latent-Infectious).
- Employed a Markov chain Monte Carlo (MCMC) algorithm within a Bayesian framework.
- Applied the model to experimental data of Rhizoctonia solani damping-off in radish, with and without Trichoderma viride.
Main Results:
- Successfully estimated the latent period of the pathogen from population data.
- Demonstrated that Trichoderma viride controls primary infection but not secondary infection.
- Showed the robustness of these findings to the inclusion of a latent period in the model.
Conclusions:
- The developed Bayesian stochastic model accurately estimates epidemiological parameters, including latent periods.
- The findings confirm the specific role of Trichoderma viride in disease management.
- The methodology is broadly applicable to various epidemiological systems and challenges.