## Abstract

This paper describes a method for estimating the seasonal variation of infection rate (or contact rate) and the trajectories of the number of susceptible, infectious and removed individuals in a deterministic SIRS model. The key idea of the proposed method is that the number of periodically varying infectives at time t can be represented as a sum of functions of the form b_{1}/(1+b_{2}(t-kT-b_{3}) ^{2}),k=...,-1,0,1,..., where b_{1}, b_{2} and b_{3} are parameters to be estimated from the incidence data, and T is the period. Given the infective trajectory, the other trajectories and the contact rate can be estimated via the model definition. The method is illustrated using cholera incidence data from three developing countries. Finally, an analysis of the sensitivity of parameter estimation for validating the obtained results using numerical analysis techniques is made.

Original language | English |
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Pages (from-to) | 161-174 |

Number of pages | 14 |

Journal | Applied Mathematics and Computation |

Volume | 118 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - Mar 9 2001 |

## Keywords

- Cholera incidence
- Numerical computation
- Seasonal variation of contact rate
- SIRS mathematical model
- Witch of Agnesi

## ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis