A state-time epidemiology model of tuberculosis: Importance of re-infection

S. Viljoen, E. Pienaar, H. J. Viljoen

Research output: Contribution to journalArticlepeer-review


An epidemiological model is presented that considers five possible states of a population: susceptible (S), exposed (W), infectious (Y), in treatment (Z) and recovered (R). In certain instances transition rates (from one state to another) depend on the time spent in the state; therefore the states W, Y and Z depend on time and length of stay in that state - similar to age-structured models. The model is particularly amenable to describe delays of exposed persons to become infectious and re-infection of exposed persons. Other transitions that depend on state time include the case finding and diagnosis, increased death rate and treatment interruption. The mathematical model comprises of a set of partial differential and ordinary differential equations. Non-steady state solutions are first presented, followed by a bifurcation study of the stationary states.

Original languageEnglish (US)
Pages (from-to)15-22
Number of pages8
JournalComputational Biology and Chemistry
StatePublished - Feb 2012


  • Drug-resistance
  • Epidemiology
  • Mathematical model
  • Partial differential equations
  • Reinfection
  • South Africa
  • State-time
  • Tuberculosis

ASJC Scopus subject areas

  • Structural Biology
  • Biochemistry
  • Organic Chemistry
  • Computational Mathematics


Dive into the research topics of 'A state-time epidemiology model of tuberculosis: Importance of re-infection'. Together they form a unique fingerprint.

Cite this