Response of a Deterministic Epidemiological System to a Stochastically Varying Environment

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 100; no. 15; pp. 9067 - 9072
• Main Authors: Truscott, J. E., Gilligan, C. A.
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 22-07-2003; National Acad Sciences
• Subjects: Beta vulgaris - microbiology; Beta vulgaris - virology; Biological Sciences; Closterovirus - pathogenicity; Critical temperature; Determinism; Disease Outbreaks - statistics & numerical data; Environment; Environmental disorders; Epidemics; Epidemiology; Epidemiology - statistics & numerical data; Fluctuations; Health risks; Infections; Inoculum; Markov analysis; Markov Chains; Modeling; Models, Theoretical; Myxomycetes - virology; Natural environment; Plant Diseases - microbiology; Plant Diseases - statistics & numerical data; Plant Diseases - virology; Seasons; Statistical variance; Stochastic models; Stochastic Processes; Temperature
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1436273100

Fluctuations in the natural environment introduce variability into the biological systems that exist within them. In this paper, we develop a model for the influence of random fluctuations in the environment on a simple epidemiological system. The model describes the infection of a dynamic host population by an environmentally sensitive pathogen and is based on the infection of sugar beet plants by the endoparasitic slime-mold vector Polymyxa betae. The infection process is switched on only when the temperature is above a critical value. We discuss some of the problems inherent in modeling such a system and analyze the resulting model by using asymptotic techniques to generate closed-form solutions for the mean and variance of the net amount of new inoculum produced within a season. In this way, the variance of temperature profile can be linked with that of the inoculum produced in a season and hence the risk of disease. We also examine the connection between the model developed in this paper and discrete Markov-chain models for weather.