A Two-strain TB model with multiple latent stages

Azizeh Jabbari, Carlos Castillo-Chavez, Fereshteh Nazari, Baojun Song, Hossein Kheiri

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A two-strain tuberculosis (TB) transmission model incorporating antibiotic-generated TB resistant strains and long and variable waiting periods within the latently infected class is introduced. The mathematical analysis is carried out when the waiting periods are modeled via parametrically friendly gamma distributions, a reasonable alternative to the use of exponential distributed waiting periods or to integral equations involving "arbitrary" distributions. The model supports a globally-asymptotically stable disease-free equilibrium when the reproduction number is less than one and an endemic equilibriums, shown to be locally asymptotically stable, or l.a.s., whenever the basic reproduction number is greater than one. Conditions for the existence and maintenance of TB resistant strains are discussed. The possibility of exogenous re-infection is added and shown to be capable of supporting multiple equilibria; a situation that increases the challenges faced by public health experts. We show that exogenous re-infection may help established resilient communities of actively-TB infected individuals that cannot be eliminated using approaches based exclusively on the ability to bring the control reproductive number just below 1.

Original languageEnglish (US)
Pages (from-to)741-785
Number of pages45
JournalMathematical Biosciences and Engineering
Volume13
Issue number4
DOIs
StatePublished - Aug 1 2016

Fingerprint

Tuberculosis
tuberculosis
Public health
Antibiotics
Integral equations
Infection
Basic Reproduction Number
Reproductive number
Multiple Equilibria
Reproduction number
Basic Reproduction number
Endemic Equilibrium
Globally Asymptotically Stable
Gamma distribution
Public Health
Asymptotically Stable
Mathematical Analysis
Model
infection
Reproduction

Keywords

  • Epidemiological models
  • Equilibria
  • Gamma distribution
  • Reproduction number
  • Resistant tuberculosis
  • Stability
  • Tuberculosis models

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Computational Mathematics
  • Agricultural and Biological Sciences(all)
  • Medicine(all)

Cite this

A Two-strain TB model with multiple latent stages. / Jabbari, Azizeh; Castillo-Chavez, Carlos; Nazari, Fereshteh; Song, Baojun; Kheiri, Hossein.

In: Mathematical Biosciences and Engineering, Vol. 13, No. 4, 01.08.2016, p. 741-785.

Research output: Contribution to journalArticle

Jabbari, Azizeh ; Castillo-Chavez, Carlos ; Nazari, Fereshteh ; Song, Baojun ; Kheiri, Hossein. / A Two-strain TB model with multiple latent stages. In: Mathematical Biosciences and Engineering. 2016 ; Vol. 13, No. 4. pp. 741-785.
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