### 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) |
---|---|

Pages (from-to) | 15-22 |

Number of pages | 8 |

Journal | Computational Biology and Chemistry |

Volume | 36 |

DOIs | |

State | Published - Feb 1 2012 |

### Fingerprint

### 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

**A state-time epidemiology model of tuberculosis : Importance of re-infection.** / Viljoen, S.; Pienaar, E.; Viljoen, Hendrik J.

Research output: Contribution to journal › Article

*Computational Biology and Chemistry*, vol. 36, pp. 15-22. https://doi.org/10.1016/j.compbiolchem.2011.11.003

}

TY - JOUR

T1 - A state-time epidemiology model of tuberculosis

T2 - Importance of re-infection

AU - Viljoen, S.

AU - Pienaar, E.

AU - Viljoen, Hendrik J

PY - 2012/2/1

Y1 - 2012/2/1

N2 - 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.

AB - 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.

KW - Drug-resistance

KW - Epidemiology

KW - Mathematical model

KW - Partial differential equations

KW - Reinfection

KW - South Africa

KW - State-time

KW - Tuberculosis

UR - http://www.scopus.com/inward/record.url?scp=84055191130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84055191130&partnerID=8YFLogxK

U2 - 10.1016/j.compbiolchem.2011.11.003

DO - 10.1016/j.compbiolchem.2011.11.003

M3 - Article

VL - 36

SP - 15

EP - 22

JO - Computational Biology and Chemistry

JF - Computational Biology and Chemistry

SN - 1476-9271

ER -