### Abstract

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 language | English (US) |
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Pages (from-to) | 15-22 |

Number of pages | 8 |

Journal | Computational Biology and Chemistry |

Volume | 36 |

DOIs | |

Publication status | Published - Feb 1 2012 |

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### Keywords

- 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

### Cite this

*Computational Biology and Chemistry*,

*36*, 15-22. https://doi.org/10.1016/j.compbiolchem.2011.11.003