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Improving process algebra model structure and parameters in infectious disease epidemiology through data mining

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Abstract

Computational models are increasingly used to assist decision-making in public health epidemiology, but achieving the best model is a complex task due to the interaction of many components and variability of parameter values causing radically different dynamics. The modelling process can be enhanced through the use of data mining techniques. Here, we demonstrate this by applying association rules and clustering techniques to two stages of modelling: identifying pertinent structures in the initial model creation stage, and choosing optimal parameters to match that model to observed data. This is illustrated through application to the study of the circulating mumps virus in Scotland, 2004-2015.

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Acknowledgments

We thank the anonymous reviewers for critical support and review of the manuscript.

Author information

Authors and Affiliations

  1. University of Ahmed Benbella Oran 1, Oran, Algeria

    Dalila Hamami & Baghdad Atmani

  2. Health Protection Scotland, 5 Cadogan St, Glasgow, G2 6QE, UK

    Ross Cameron & Kevin G Pollock

  3. University of Stirling, Stirling, UK

    Carron Shankland

Authors
  1. Dalila Hamami
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  2. Baghdad Atmani
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  3. Ross Cameron
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  4. Kevin G Pollock
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  5. Carron Shankland
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Corresponding author

Correspondence to Dalila Hamami.

Appendices

Appendix A: Additional figures

Figure 8 (resp. Figs. 9 and 10) shows that K-means clustering applied to mumps confirmed cases and plotted by Age (resp. MMR status and Sex) is not meaningful for the model where both clusters depicted similar age groups (resp. similar distribution of MMR status and Sex).

Fig. 8
figure 8

K-means clustering applied to mumps confirmed cases OneYearOneBoardVaccStatus: Clusters vs Age

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Fig. 9
figure 9

K-means clustering applied to mumps confirmed cases OneYearOneBoardVaccStatus: Clusters vs MMR Status

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Fig. 10
figure 10

K-means clustering applied to mumps confirmed cases OneYearOneBoardVaccStatus: Clusters vs Sex

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Appendix: B: Model

  1. 1.

    mu = 0.000037;

  2. 2.

    beta1 = 0.7;

  3. 3.

    beta2 = 0.9;

  4. 4.

    beta3 = 0.4;

  5. 5.

    mu1 = 0.0000021;

  6. 6.

    mu2 = 0.0000028;

  7. 7.

    mu3 = 0.000025;

  8. 8.

    alpha = 0.05;

  9. 9.

    gamma = 0.143;

  10. 10.

    lambda = 0.07;

  11. 11.

    tau = 0.00034;

  12. 12.

    delta = tau/2;

  13. 13.

    sizeOutside = 110000;

  14. 14.

    sizeLocal = 5300000;

  15. 15.

    location world : size = 5200000 , type = compartment;

  16. 16.

    location Local in world: size = sizeLocal, type = compartment;

  17. 17.

    location Local in world: size = sizeLocal, type = compartment;

  18. 18.

    location Outside in world : size = sizeOutside, type = compartment;

  19. 19.

    thigh = 4;

  20. 20.

    tlow = 9;

  21. 21.

    month = floor(time/30);

  22. 22.

    season_time = 1-H(((month - 12*floor(month/12)) - tlow)* (thigh-(month - 12*floor(month/12))) );

  23. 23.

    N = (S1@Local + E@Local + I@Local + R@Local + S2@Local + MMR1@Local + MMR2@Local);Kinetic Laws

  24. 24.

    kineticLawOf BIRTH1: mu1 * N;

  25. 25.

    kineticLawOf BIRTH2: mu2 * N;

  26. 26.

    kineticLawOf BIRTH3: mu3 * N;

  27. 27.

    kineticLawOf MMR1_S2: MMR1@Local *tau;

  28. 28.

    kineticLawOf MMR2_S2: MMR2@Local *delta;

  29. 29.

    kineticLawOf Death_MMR1 : mu * MMR1@Local;

  30. 30.

    kineticLawOf Death_MMR2 : mu * MMR2@Local;

  31. 31.

    kineticLawOf immigration : lambda/10000;

  32. 32.

    kineticLawOf S1_E: (beta1 * S1@Local * I@Local)/N * (season_time) + (1-season_time)*(beta3 * S1@Local * I@Local)/N ;

  33. 33.

    kineticLawOf S2_E: (beta2 * S2@Local * I@Local)/N * (season_time) + (1-season_time)* (beta3 * S2@Local * I@Local)/N;

  34. 34.

    kineticLawOf E_I: alpha * E@Local;

  35. 35.

    kineticLawOf I_R: gamma * I@Local;

  36. 36.

    kineticLawOf Death_S1: mu * S1@Local;

  37. 37.

    kineticLawOf Death_I: mu * I@Local ;

  38. 38.

    kineticLawOf Death_E: mu * E@Local;

  39. 39.

    kineticLawOf Death_S2: mu * S2@Local;

  40. 40.

    kineticLawOf Death_R: mu * R@Local;Species

  41. 41.

    S1 = (BIRTH1,1) >> S1@Local + (S1_E,1) << S1@Local + Death_S1 << S1@Local;

  42. 42.

    S2 = (S2_E,1) << S2@Local + Death_S2 << S2@Local + (MMR2_S2,1) >> S2@Local + (MMR1_S2,1) >> S2@Local;

  43. 43.

    E = (S1_E,1) >> E@Local + (S2_E,1) >> E@Local + (E_I,1) << E@Local+ Death_E << E@Local;

  44. 44.

    I = (E_I,1) >> I@Local + (I_R,1) << I@Local + Death_I << I@Local+ immigration[Outside → Local] (.)I + (S1_E,1) (.) I + (S2_E,1) (.) I;

  45. 45.

    R = (I_R,1) >> R@Local+ Death_R << R@Local ;

  46. 46.

    MMR1 = (BIRTH2,1) >> MMR1@Local + (MMR1_S2,1) << MMR1@Local+ Death_MMR1 << ;

  47. 47.

    MMR2 = (BIRTH3,1) >> MMR2@Local + (MMR2_S2,1) << MMR2@Local+ Death_MMR2 << ;Model component

  48. 48.

    S1@Local[1100000] < ∗ > S2@Local[0] < ∗ > E@Local[0] < ∗ > I@Local[20]< ∗ > R@Local[3218600] < ∗ > MMR1@Local[273541] < ∗ > MMR2@Local[250000] < ∗ > I@Outside[10000]

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Hamami, D., Atmani, B., Cameron, R. et al. Improving process algebra model structure and parameters in infectious disease epidemiology through data mining. J Intell Inf Syst 52, 477–499 (2019). https://doi.org/10.1007/s10844-017-0476-1

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