Abstract
Simple models for disease transmission that include immigration of infective individuals and variable population size are constructed and analyzed. A model with a general contact rate for a disease that confers no immunity admits a unique endemic equilibrium that is globally stable. A model with mass action incidence for a disease in which infectives either die or recover with permanent immunity has the same qualitative behavior. This latter result is proved by reducing the system to an integro-differential equation. If mass action incidence is replaced by a general contact rate, then the same result is proved locally for a disease that causes fatalities. Threshold-like results are given, but in the presence of immigration of infectives there is no disease-free equilibrium. A considerable reduction of infectives is suggested by the incorporation of screening and quarantining of infectives in a model for HIV transmission in a prison system.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 143-154 |
| Number of pages | 12 |
| Journal | Mathematical Biosciences |
| Volume | 171 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2001 |
| Externally published | Yes |
Keywords
- Epidemic model
- Global stability
- Immigration
- Quarantine
- Threshold
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics