On the role of variable latent periods in mathematical models for tuberculosis

Zhilan Feng, Wenzhang Huang, Carlos Castillo-Chavez

Research output: Contribution to journalArticle

62 Scopus citations

Abstract

The qualitative behaviors of a system of ordinary differential equations and a system of differential-integral equations, which model the dynamics of disease transmission for tuberculosis (TB), have been studied. It has been shown that the dynamics of both models are governed by a reproductive number. All solutions converge to the origin (the disease-free equilibrium) when this reproductive number is less than or equal to the critical value one. The disease-free equilibrium is unstable and there exists a unique positive (endemic) equilibrium if the reproductive number exceeds one. Moreover, the positive equilibrium is stable. Our results show that the qualitative behaviors predicted by the model with arbitrarily distributed latent stage are similar to those given by the TB model with an exponentially distributed period of latency.

Original languageEnglish (US)
Pages (from-to)425-452
Number of pages28
JournalJournal of Dynamics and Differential Equations
Volume13
Issue number2
DOIs
StatePublished - Jan 1 2001
Externally publishedYes

Keywords

  • Distributed delay
  • Global stability
  • Mathematical models
  • Tuberculosis

ASJC Scopus subject areas

  • Analysis

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