Frequency-Dependent Disease Transmission and the Dynamics of the Silene-Ustilago Host-Pathogen System

Abstract

Models incorporating density-dependent disease transmission functions generally provide a good fit for airborne and directly transmitted bacterial or viral diseases. However, the transmission dynamics of sexually transmitted and vector-borne diseases are likely to be frequency- rather than density- dependent, which results in qualitatively different dynamics. Here, we present analyses of a basic epidemiological model in which the transmission process is represented as a function of the population disease frequency. In an extension of the basic model, we consider disease transmission as a probability function that assumes that the chance of becoming infected increases with the number of vector contacts. Stability analyses show that host-pathogen coexistence is possible in vector-transmitted and sexually transmitted disease systems in which transmission is likely to be frequency-dependent; the potential for stable coexistence is greatest for intermediate rates of disease spread and weak density dependence of host growth rate. Extension of the basic frequency-dependent model to allow for multiple contacts among hosts indicates that parameter ranges within which coexistence is predicted are thereby broadened. [KEYWORDS: Parasite population interactions; infectious-diseases; density-dependence; viscaria-vulgaris; epidemic models; salvia-lyrata; violacea; stability; patterns; biology]