### Abstract

Mathematical modeling of infectious diseases is necessary to study patterns of transmission and propagation that can potentially help public health officials to make better decisions to mitigate epidemic outbreaks. Both discrete and continuous population models can give insight into the approximations of the modeling approaches we implement. Metapopulation models in which we examine disease dynamics on separate patches and allow movement of the population between the patches have become increasingly popular to model the spread of diseases over geographically distinct regions. We use the forward Kolmogorov equations and present a formal proof that states that the deterministic model is in fact the expected value of the continuous-time Markov chain stochastic model trials. We show the connection between both modeling approaches in an SIS metapopulation model. We present the results of simulations to illustrate the results for different values of R_{0}, the basic reproductive number.

Original language | English (US) |
---|---|

Pages (from-to) | 108-118 |

Number of pages | 11 |

Journal | Mathematical Scientist |

Volume | 41 |

Issue number | 2 |

State | Published - Dec 1 2016 |

### Fingerprint

### Keywords

- Continuous-time Markov chain
- Forward Kolmogorov equation
- Metapopulation model
- Probability generating function
- SIS model
- Stochastic model

### ASJC Scopus subject areas

- Materials Science(all)

### Cite this

*Mathematical Scientist*,

*41*(2), 108-118.

**Kolmogorov equations applied to an SIS-coupled epidemiological model.** / Cruz-Aponte, Mayteé; Wirkus, Stephen.

Research output: Contribution to journal › Article

*Mathematical Scientist*, vol. 41, no. 2, pp. 108-118.

}

TY - JOUR

T1 - Kolmogorov equations applied to an SIS-coupled epidemiological model

AU - Cruz-Aponte, Mayteé

AU - Wirkus, Stephen

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Mathematical modeling of infectious diseases is necessary to study patterns of transmission and propagation that can potentially help public health officials to make better decisions to mitigate epidemic outbreaks. Both discrete and continuous population models can give insight into the approximations of the modeling approaches we implement. Metapopulation models in which we examine disease dynamics on separate patches and allow movement of the population between the patches have become increasingly popular to model the spread of diseases over geographically distinct regions. We use the forward Kolmogorov equations and present a formal proof that states that the deterministic model is in fact the expected value of the continuous-time Markov chain stochastic model trials. We show the connection between both modeling approaches in an SIS metapopulation model. We present the results of simulations to illustrate the results for different values of R0, the basic reproductive number.

AB - Mathematical modeling of infectious diseases is necessary to study patterns of transmission and propagation that can potentially help public health officials to make better decisions to mitigate epidemic outbreaks. Both discrete and continuous population models can give insight into the approximations of the modeling approaches we implement. Metapopulation models in which we examine disease dynamics on separate patches and allow movement of the population between the patches have become increasingly popular to model the spread of diseases over geographically distinct regions. We use the forward Kolmogorov equations and present a formal proof that states that the deterministic model is in fact the expected value of the continuous-time Markov chain stochastic model trials. We show the connection between both modeling approaches in an SIS metapopulation model. We present the results of simulations to illustrate the results for different values of R0, the basic reproductive number.

KW - Continuous-time Markov chain

KW - Forward Kolmogorov equation

KW - Metapopulation model

KW - Probability generating function

KW - SIS model

KW - Stochastic model

UR - http://www.scopus.com/inward/record.url?scp=85008684236&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85008684236&partnerID=8YFLogxK

M3 - Article

VL - 41

SP - 108

EP - 118

JO - Mathematical Scientist

JF - Mathematical Scientist

SN - 0312-3685

IS - 2

ER -