A Simple Epidemic Model with Surprising Dynamics - F. Berezovskaya; G. Karev; Baojun Song; Carlos Castillo-Chavez (Mathematical Biosciences and Engineering)
A simple model incorporating demographic and epidemiologicalprocesses is explored. Four re-parameterized quantities the basicdemographic reproductive number ($\R_d$), the basic epidemiologicalreproductive number ($\R_0$), the ratio ($ν$) between the averagelife spans of susceptible and infective class, and the relativefecundity of infectives ($θ$), are utilized in qualitativeanalysis. Mathematically, non-analytic vector fields are handled byblow-up transformations to carry out a complete and global dynamicalanalysis. A family of homoclinics is found, suggesting that adisease outbreak would be ignited by a tiny number of infectiousindividuals.