The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm

Kavyu Mary Kamina; Samuel Mwalili; Anthony Wanjoya

doi:doi:10.11648/j.ijdsa.20190506.12

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The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm

Kavyu Mary Kamina, Samuel Mwalili, Anthony Wanjoya

Published in International Journal of Data Science and Analysis (Volume 5, Issue 6)

Received: 8 October 2019 Accepted: 28 October 2019 Published: 4 November 2019

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Abstract

Mathematical modeling of disease has been an indispensable tool in accounting for disease transmission dynamics as well as disease spread. Epidemiological disease models have been used to explain the dynamics of HIV/AIDS in the population from the early 1900s. The models developed however faced considerable challenges ranging from inaccurate representation of natural data for deterministic models, to methods of forecasting such as statistical extrapolation which assumes that current conditions will prevail which is not always the case. Despite the spread of HIV/AIDS having been explored widely, not much literature is available on the Gillespie Algorithm based SIR model. This algorithm is able to give a statistically correct of the course of a disease with initial conditions to begin with and propensity functions to update the system. The purpose of this paper is to build on the concept of Gillespie's Algorithm based SIR models by developing a stochastic SIR model to simulate disease evolution in the population setting. The values produced through simulation by the model developed in this paper using a tau value as the time step of the model were compared to HIV/AIDS data from 1985 to 2018, given by NACC. We conclude that the simulated model reflects reality.

Published in	International Journal of Data Science and Analysis (Volume 5, Issue 6)
DOI	10.11648/j.ijdsa.20190506.12
Page(s)	117-122
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Stochastic, Simulation, Deterministic, SIR Model, Continuous-Time Markov Chain, Gillespie's Algorithm Models

References

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APA Style

Kavyu Mary Kamina, Samuel Mwalili, Anthony Wanjoya. (2019). The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm. International Journal of Data Science and Analysis, 5(6), 117-122. https://doi.org/10.11648/j.ijdsa.20190506.12

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ACS Style

Kavyu Mary Kamina; Samuel Mwalili; Anthony Wanjoya. The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm. Int. J. Data Sci. Anal. 2019, 5(6), 117-122. doi: 10.11648/j.ijdsa.20190506.12

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AMA Style

Kavyu Mary Kamina, Samuel Mwalili, Anthony Wanjoya. The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm. Int J Data Sci Anal. 2019;5(6):117-122. doi: 10.11648/j.ijdsa.20190506.12

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@article{10.11648/j.ijdsa.20190506.12,
  author = {Kavyu Mary Kamina and Samuel Mwalili and Anthony Wanjoya},
  title = {The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {6},
  pages = {117-122},
  doi = {10.11648/j.ijdsa.20190506.12},
  url = {https://doi.org/10.11648/j.ijdsa.20190506.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190506.12},
  abstract = {Mathematical modeling of disease has been an indispensable tool in accounting for disease transmission dynamics as well as disease spread. Epidemiological disease models have been used to explain the dynamics of HIV/AIDS in the population from the early 1900s. The models developed however faced considerable challenges ranging from inaccurate representation of natural data for deterministic models, to methods of forecasting such as statistical extrapolation which assumes that current conditions will prevail which is not always the case. Despite the spread of HIV/AIDS having been explored widely, not much literature is available on the Gillespie Algorithm based SIR model. This algorithm is able to give a statistically correct of the course of a disease with initial conditions to begin with and propensity functions to update the system. The purpose of this paper is to build on the concept of Gillespie's Algorithm based SIR models by developing a stochastic SIR model to simulate disease evolution in the population setting. The values produced through simulation by the model developed in this paper using a tau value as the time step of the model were compared to HIV/AIDS data from 1985 to 2018, given by NACC. We conclude that the simulated model reflects reality.},
 year = {2019}
}

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TY  - JOUR
T1  - The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm
AU  - Kavyu Mary Kamina
AU  - Samuel Mwalili
AU  - Anthony Wanjoya
Y1  - 2019/11/04
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190506.12
DO  - 10.11648/j.ijdsa.20190506.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 117
EP  - 122
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190506.12
AB  - Mathematical modeling of disease has been an indispensable tool in accounting for disease transmission dynamics as well as disease spread. Epidemiological disease models have been used to explain the dynamics of HIV/AIDS in the population from the early 1900s. The models developed however faced considerable challenges ranging from inaccurate representation of natural data for deterministic models, to methods of forecasting such as statistical extrapolation which assumes that current conditions will prevail which is not always the case. Despite the spread of HIV/AIDS having been explored widely, not much literature is available on the Gillespie Algorithm based SIR model. This algorithm is able to give a statistically correct of the course of a disease with initial conditions to begin with and propensity functions to update the system. The purpose of this paper is to build on the concept of Gillespie's Algorithm based SIR models by developing a stochastic SIR model to simulate disease evolution in the population setting. The values produced through simulation by the model developed in this paper using a tau value as the time step of the model were compared to HIV/AIDS data from 1985 to 2018, given by NACC. We conclude that the simulated model reflects reality.
VL  - 5
IS  - 6
ER  -

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Author Information

Kavyu Mary Kamina

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Samuel Mwalili

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Wanjoya

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Kavyu Mary Kamina, Samuel Mwalili, Anthony Wanjoya. (2019). The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm. International Journal of Data Science and Analysis, 5(6), 117-122. https://doi.org/10.11648/j.ijdsa.20190506.12

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ACS Style

Kavyu Mary Kamina; Samuel Mwalili; Anthony Wanjoya. The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm. Int. J. Data Sci. Anal. 2019, 5(6), 117-122. doi: 10.11648/j.ijdsa.20190506.12

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AMA Style

Kavyu Mary Kamina, Samuel Mwalili, Anthony Wanjoya. The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm. Int J Data Sci Anal. 2019;5(6):117-122. doi: 10.11648/j.ijdsa.20190506.12

Copy | Download

@article{10.11648/j.ijdsa.20190506.12,
  author = {Kavyu Mary Kamina and Samuel Mwalili and Anthony Wanjoya},
  title = {The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {6},
  pages = {117-122},
  doi = {10.11648/j.ijdsa.20190506.12},
  url = {https://doi.org/10.11648/j.ijdsa.20190506.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190506.12},
  abstract = {Mathematical modeling of disease has been an indispensable tool in accounting for disease transmission dynamics as well as disease spread. Epidemiological disease models have been used to explain the dynamics of HIV/AIDS in the population from the early 1900s. The models developed however faced considerable challenges ranging from inaccurate representation of natural data for deterministic models, to methods of forecasting such as statistical extrapolation which assumes that current conditions will prevail which is not always the case. Despite the spread of HIV/AIDS having been explored widely, not much literature is available on the Gillespie Algorithm based SIR model. This algorithm is able to give a statistically correct of the course of a disease with initial conditions to begin with and propensity functions to update the system. The purpose of this paper is to build on the concept of Gillespie's Algorithm based SIR models by developing a stochastic SIR model to simulate disease evolution in the population setting. The values produced through simulation by the model developed in this paper using a tau value as the time step of the model were compared to HIV/AIDS data from 1985 to 2018, given by NACC. We conclude that the simulated model reflects reality.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - The Modeling of a Stochastic SIR Model for HIV/AIDS Epidemic Using Gillespie's Algorithm
AU  - Kavyu Mary Kamina
AU  - Samuel Mwalili
AU  - Anthony Wanjoya
Y1  - 2019/11/04
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190506.12
DO  - 10.11648/j.ijdsa.20190506.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 117
EP  - 122
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190506.12
AB  - Mathematical modeling of disease has been an indispensable tool in accounting for disease transmission dynamics as well as disease spread. Epidemiological disease models have been used to explain the dynamics of HIV/AIDS in the population from the early 1900s. The models developed however faced considerable challenges ranging from inaccurate representation of natural data for deterministic models, to methods of forecasting such as statistical extrapolation which assumes that current conditions will prevail which is not always the case. Despite the spread of HIV/AIDS having been explored widely, not much literature is available on the Gillespie Algorithm based SIR model. This algorithm is able to give a statistically correct of the course of a disease with initial conditions to begin with and propensity functions to update the system. The purpose of this paper is to build on the concept of Gillespie's Algorithm based SIR models by developing a stochastic SIR model to simulate disease evolution in the population setting. The values produced through simulation by the model developed in this paper using a tau value as the time step of the model were compared to HIV/AIDS data from 1985 to 2018, given by NACC. We conclude that the simulated model reflects reality.
VL  - 5
IS  - 6
ER  -

Copy | Download