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A stochastic model of contagion with different individual types

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  • 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.

    Mathematics Subject Classification: 92D30, 91B70.

    Citation:

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  • Figure 1.  The probability density functions and the complementary cumulative distribution functions of the contagion duration in Application 1

    Figure 2.  The probability mass functions of the number of individual afflictions in Application 1

    Figure 3.  The probability density functions and the complementary cumulative distribution functions of the contagion duration in Application 2

    Figure 4.  The probability mass functions of the number of individual afflictions in Application 2

    Figure 5.  The probability density functions and the complementary cumulative distribution functions of the contagion duration in Application 3

    Figure 6.  The probability mass functions of the number of individual afflictions in Application 3

    Table 1.  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
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    Table 2.  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
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    Table 3.  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
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