Volume 43 Issue 4
Apr.  2022
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YAN Qinling, TANG Sanyi. Dynamic Changes of Influenza A/H1N1 Epidemic Evaluated Based on the Kolmogorov Forward Equation[J]. Applied Mathematics and Mechanics, 2022, 43(4): 435-444. doi: 10.21656/1000-0887.420243
Citation: YAN Qinling, TANG Sanyi. Dynamic Changes of Influenza A/H1N1 Epidemic Evaluated Based on the Kolmogorov Forward Equation[J]. Applied Mathematics and Mechanics, 2022, 43(4): 435-444. doi: 10.21656/1000-0887.420243

Dynamic Changes of Influenza A/H1N1 Epidemic Evaluated Based on the Kolmogorov Forward Equation

doi: 10.21656/1000-0887.420243
  • Received Date: 2021-08-13
  • Accepted Date: 2021-09-13
  • Rev Recd Date: 2021-09-13
  • Available Online: 2022-03-25
  • Publish Date: 2022-04-01
  • The individual-based infectious disease models show the important role of stochasticity in infectious disease prevention and control. To study these models and then determine the ranges of predictive variables, an increasingly common approach needs event-driven massive repetitive stochastic simulations. The study of the individual-based infectious disease models based on the Kolmogorov forward equation (KFE), not only could overcome the difficulty of repeated simulations, but could consider the probability of each state simultaneously. Therefore, according to the data of 2009 influenza A/H1N1 in the Xi’an 8th Hospital, to determine the rate of behavior change, an individual decision-making psychological model was established based on social network. Further, in order to obtain the probability distribution of each state in the process of infectious disease transmission, based on the modified individual SIR model, the KFE was derived through the Markov processes. The results show that, the numerical solution of the KFE gives the probability distribution of each state, the most serious period and the corresponding probability in the outbreak process of epidemic infectious diseases, so as to help understand the transmission process of A/H1N1 epidemic more quickly and accurately, which is valuable for the efficient prevention and control of A/H1N1 epidemic.

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  • [1]
    BARTLETT M S. Deterministic and stochastic models for recurrent epidemics[C]//Process Third Berkley Sympathetic Mathematical Statstics and Probalibity. 1956, 4(1956): 81-108.
    [2]
    RAND D A, WILSON H B. Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics[J]. Proceedings of the Royal Society B, 1991, 246(1316): 179-184.
    [3]
    FOX G A. Life-history evolution and demographic stochasticity[J]. Ecology and Evolution, 1993, 7(1): 1-14.
    [4]
    GRENFELL B T, WILSON K, FINKENSTA B F, et al. Noise and determinism in synchronized sheep dynamics[J]. Nature, 1998, 394(6694): 674-677.
    [5]
    KEELING M J, WILSON H B, PACALA S W. Re-interpreting space time-lags and functional responses in ecological models[J]. Science, 2000, 290(5497): 1758-1761.
    [6]
    GILLESPIE D T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions[J]. Journal of Computational Physics, 1976, 22(4): 403-434.
    [7]
    RENSHAW E. Modelling Biological Populations in Space and Time[M]. Cambridge: Cambridge University Press, 1995.
    [8]
    VAN KAMPEN N G. Stochastic Processes in Physics and Chemistry[M]. Amsterdam: Noth-Holland, 1983.
    [9]
    JENKINSON G, GOUTSIAS J. Numerical integration of the master equation in some models of stochastic epidemiology[J]. PLoS ONE, 2012, 7(5): e36160.
    [10]
    KEELING M J, ROSS J V. On methods for studying stochastic disease dynamics[J]. Journal of Royal Society Interface, 2008, 5(19): 171-181.
    [11]
    DIECKMANN U, LAW R. The dynamical theory of coevolution: a derivation from stochastic ecological processes[J]. Journal of Mathematical Biology, 1996, 34(5/6): 579-612.
    [12]
    ALONSO D, MCKANE A. Extinction dynamics in mainland-island metapopulations: an N-patch stochastic model[J]. Bulletin of Mathematical Biology, 2002, 64(5): 913-958.
    [13]
    ALONSO D, MCKANE A J, PASCUAL M. Stochastic amplification in epidemics[J]. Journal of the Royal Society Interface, 2006, 4(14): 575-582.
    [14]
    VIET A, MEDLEY G F. Stochastic dynamics of immunity in small populations: a general framework[J]. Mathematical Biosciences, 2006, 200(1): 28-43.
    [15]
    POLETTI P, CAPRILE B, AJELLI M, et al. Spontaneous behavioural changes in response to epidemics[J]. Journal of Theoretical Biology 2009, 260(1): 31-40.
    [16]
    POLETTI P. Human behaviour in epidemic modelling[D]. PhD Thesis. Trento: University of Trento, 2010.
    [17]
    DURHAM D P, CASMAN E A. Incorporating individual health-protective decisions into disease transmission models: a mathematical framework[J]. Journal of Royal Society Interface, 2012, 9(68): 562-570.
    [18]
    YAN Q L, TANG S Y, XIAO Y N. Impact of individual behaviour change on the spread of emerging infectious diseases[J]. Statistics in Medicine, 2018, 37(6): 948-969.
    [19]
    VAN KAMPEN N G. Stochastic processes in physics and chemistry[J]. Physics Today, 1983, 36(2): 78-80.
    [20]
    GILLESPIE D T. The chemical Langevin equation[J]. Journal of Chemical Physics, 2000, 113(1): 297-306.
    [21]
    KERMACK W O, MCKENDRICK A G. A contribution to the mathematical theory of epidemics[J]. Bulletin of Mathematical Biology, 1991, 53(1/2): 57-87.
    [22]
    BECAR R, GONZALEZ P A, VASQUEZ Y. Fermionic greybody factors of two and five-dimensional dilatonic black holes[J]. European Physical Journal C, 2014, 74(8): 1-8.
    [23]
    WANG W D, ZHAO X Q. Threshold dynamics for compartmental epidemic models in periodic environments[J]. Journal of Dynamics and Differential Equations, 2008, 20(3): 699-717.
    [24]
    WANG X, XIAO Y N, WANG J R, et al. Stochastic disease dynamics of a hospital infection model[J]. Mathematical Biosciences, 2013, 241(1): 115-124.
    [25]
    KEELING M J, ROHANI P. Modeling Infectious Diseases in Humans and Animals[M]. Princeton: Princeton University Press, 2007.
    [26]
    CHAMPION V L, SKINNER C S. In Health Behaviour and Health Education: Theory, Research, and Practice [M]. 4th ed. San Francisco: John Wiley & Sons, 2008.
    [27]
    DURHAM D P, CASMAN E A. Incorporating individual health-protective decisions into disease transmission models: a mathematical framework[J]. Journal of Royal Society Interface, 2012, 9(2012): 562-570.
    [28]
    WATTS D J, STROGATZ S H. Collective dynamics of 'small-world' networks[J]. Nature, 1998, 393(1998): 440-442.
    [29]
    NEWMAN M E J. The structure and function of complex networks[J]. SIAM Review, 2003, 45(2): 167-256.
    [30]
    HOLLAND M D, HASTINGS A. Strong effect of dispersal network structure on ecological dynamics[J]. Nature, 2012, 456(2012): 792-794.
    [31]
    NEWMAN M E J, WATTS D J. Renormalization group analysis of the small-world network model[J]. Physics Letters A, 1999, 263(1999): 341-346.
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