The basic reproduction number in some discrete-time epidemic models

• Published in: Journal of difference equations and applications Vol. 14; no. 10-11; pp. 1127 - 1147
• Main Authors: Allen, Linda J.S., van den Driessche, P.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01.10.2008
• Subjects: basic reproduction number; chytridiomycosis; discrete-time epidemic model; epidemic model on patches; hantavirus; next generation matrix
• ISSN: 1023-6198; 1563-5120
• DOI: 10.1080/10236190802332308

The next generation matrix approach for calculating the basic reproduction number is summarized for discrete-time epidemic models. This approach is applied to six disease models developed for the study of two emerging wildlife diseases: hantavirus in rodents and chytridiomycosis in amphibians. Two of the models include discrete spatial patches. For each model, is calculated in terms of the model parameters. For , if a small number of infectives is introduced, then the wildlife disease dies out. Global stability of the disease-free equilibrium is verified for a special case of the SI hantavirus model when . In addition, a numerical example indicates that there is a transcritical bifurcation at , with the disease dying out if but tending to an endemic level if .