F. Berezovskaya - Department of Mathematics, Howard University, Washington D.C., 20059, United States (email)
Abstract: A simple model incorporating demographic and epidemiological processes is explored. Four re-parameterized quantities the basic demographic reproductive number ($\R_d$), the basic epidemiological reproductive number ($\R_0$), the ratio ($\nu$) between the average life spans of susceptible and infective class, and the relative fecundity of infectives ($\theta$), are utilized in qualitative analysis. 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 individuals.
Keywords: Epidemic model, dynamical system, bifurcation analysis, global
Received: July 2004; Accepted: August 2004; Available Online: November 2004.
2015 5-year IF1.087