A simple epidemic model with surprising dynamics
Related Experiment Video
Updated: Jun 14, 2026

Following the Dynamics of Structural Variants in Experimentally Evolved Populations
Published on: February 3, 2023
Faina Berezovsky1, Georgy Karev, Baojun Song
1Mathematical Department Howard University, Washington D.C. 20059. fsberezo@hotmail.com.
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 (v) 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.
Related Concept Videos
Modeling with Differential Equations
Population Growth
Exponential Equations for Modeling Growth
Steps in Outbreak Investigation
Causality in Epidemiology
Pharmacodynamic Models: Logarithmic Concentration–Effect Model

