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Zbl 1061.92052
Berezovsky, Faina; Karev, Georgy; Song, Baojun; Castillo-Chavez, Carlos
A simple epidemic model with surprising dynamics.
(English)
[J] Math. Biosci. Eng. 2, No. 1, 133-152 (2005). ISSN 1547-1063; ISSN 1551-0018/e

Summary: A simple model incorporating demographic and epidemiological processes is explored. Four re-parameterized quantities, the basic demographic reproductive number $({\cal R}_d)$, the basic epidemiological reproductive number $({\cal R}_0)$, the ratio $(\nu)$ between the average life spans of susceptible and infective class, and the relative fecundity of infectives $(\theta)$, are utilized in the qualitative analysis.\par Mathematically, non-analytic vector fields are handled by blow-up transformations to carry out a complete and global dynamical analysis. A family of homoclinics is found, suggesting that a disease outbreak would be ignited by a tiny number of infectious individuais.
MSC 2000:
*92D30 Epidemiology
37N25 Dynamical systems in biology
34C37 Homoclinic and heteroclinic solutions of ODE
37G35 Attractors and their bifurcations
34D23 Global stability

Keywords: rescaling; phase portraits

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