# American Institute of Mathematical Sciences

September  2020, 16(5): 2175-2193. doi: 10.3934/jimo.2019049

## A stochastic model of contagion with different individual types

 1 Underwood International College, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 03722, Korea 2 Department of Mathematics, University of Seoul, 163 Seoulsiripdae-ro, Dongdaemun-gu, Seoul, 02504, Korea 3 Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, Korea

* Corresponding author

Received  April 2018 Revised  December 2018 Published  May 2019

We develop a stochastic model of contagion with two individual types by extending an archetypal SIS CTMC model. Our results include the analyses of the contagion duration and the number of individual afflictions. Numerical applications with the minority and majority types are provided to consider various contagions.

Citation: Geofferey Jiyun Kim, Jerim Kim, Bara Kim. A stochastic model of contagion with different individual types. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2175-2193. doi: 10.3934/jimo.2019049
##### References:

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##### References:
The probability density functions and the complementary cumulative distribution functions of the contagion duration in Application 1
The probability mass functions of the number of individual afflictions in Application 1
The probability density functions and the complementary cumulative distribution functions of the contagion duration in Application 2
The probability mass functions of the number of individual afflictions in Application 2
The probability density functions and the complementary cumulative distribution functions of the contagion duration in Application 3
The probability mass functions of the number of individual afflictions in Application 3
Parameter values for Application 1
 $\beta_{11}$ $\beta_{12}$ $\beta_{21}$ $\beta_{22}$ $\gamma_{1}$ $\gamma_{2}$ (ⅰ) 0.2 0.1313 2.625 1.25 1 1 (ⅱ) 0.15 0.1313 2.625 2.25 1 1
 $\beta_{11}$ $\beta_{12}$ $\beta_{21}$ $\beta_{22}$ $\gamma_{1}$ $\gamma_{2}$ (ⅰ) 0.2 0.1313 2.625 1.25 1 1 (ⅱ) 0.15 0.1313 2.625 2.25 1 1
Parameter values of Application 2
 $\beta_{11}$ $\beta_{12}$ $\beta_{21}$ $\beta_{22}$ $\gamma_{1}$ $\gamma_{2}$ (ⅰ) 0.25 0.1313 2.625 0.25 1 1 (ⅱ) 0.25 0.1313 2.625 0.25 1.02 0.6
 $\beta_{11}$ $\beta_{12}$ $\beta_{21}$ $\beta_{22}$ $\gamma_{1}$ $\gamma_{2}$ (ⅰ) 0.25 0.1313 2.625 0.25 1 1 (ⅱ) 0.25 0.1313 2.625 0.25 1.02 0.6
Parameter values of Application 3
 $\beta_{11}$ $\beta_{12}$ $\beta_{21}$ $\beta_{22}$ $\gamma_{1}$ $\gamma_{2}$ (ⅰ) 0.5 0 0 0.5 1 1 (ⅱ) 0.25 0.1313 2.625 0.25 1 1 (iii) 0 0.2625 5.25 0 1 1
 $\beta_{11}$ $\beta_{12}$ $\beta_{21}$ $\beta_{22}$ $\gamma_{1}$ $\gamma_{2}$ (ⅰ) 0.5 0 0 0.5 1 1 (ⅱ) 0.25 0.1313 2.625 0.25 1 1 (iii) 0 0.2625 5.25 0 1 1
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