Diseases with chronic stage in a population with varying size

Maia Martcheva, Carlos Castillo-Chavez

Research output: Contribution to journalArticle

51 Citations (Scopus)

Abstract

An epidemiological model of hepatitis C with a chronic infectious stage and variable population size is introduced. A non-structured baseline ODE model which supports exponential solutions is discussed. The normalized version where the unknown functions are the proportions of the susceptible, infected, and chronic individuals in the total population is analyzed. It is shown that sustained oscillations are not possible and the endemic proportions either approach the disease-free or an endemic equilibrium. The expanded model incorporates the chronic age of the individuals. Partial analysis of this age-structured model is carried out. The global asymptotic stability of the infection-free state is established as well as local asymptotic stability of the endemic non-uniform steady state distribution under some additional conditions. A numerical method for the chronic-age-structured model is introduced. It is shown that this numerical scheme is consistent and convergent of first order. Simulations based on the numerical method suggest that in the structured case the endemic equilibrium may be unstable and sustained oscillations are possible. Closer look at the reproduction number reveals that treatment strategies directed towards speeding up the transition from acute to chronic stage in effect contribute to the eradication of the disease.

Original languageEnglish (US)
Pages (from-to)1-25
Number of pages25
JournalMathematical Biosciences
Volume182
Issue number1
DOIs
StatePublished - Mar 2003
Externally publishedYes

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Age-structured Model
Endemic Equilibrium
Proportion
Chronic Disease
Numerical Methods
Oscillation
Disease Eradication
Local Asymptotic Stability
Reproduction number
Epidemiological Model
Steady-state Distribution
Global Asymptotic Stability
Hepatitis C
Population Density
Population Size
Acute
Numerical Scheme
Population
Reproduction
Infection

Keywords

  • Chronic stage
  • Difference scheme
  • Disease-age structure
  • Hepatitis C
  • Numerical methods
  • Sustained oscillations
  • Variable infectivity
  • Variable population size

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Diseases with chronic stage in a population with varying size. / Martcheva, Maia; Castillo-Chavez, Carlos.

In: Mathematical Biosciences, Vol. 182, No. 1, 03.2003, p. 1-25.

Research output: Contribution to journalArticle

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