Epidemic Dynamics Modeling and Analysis

  • Ming LiuEmail author
  • Jie Cao
  • Jing Liang
  • MingJun Chen


Disastrous epidemic such as SARS, H1N1, or smallpox released by some terrorists can significantly affect people’s life. The outbreak of infections in Europe in 2011 is another example. The infection, from a strain of Escherichia coli, can lead to kidney failure and death and is difficult to treat with antibiotics. A recent example of epidemic outbreak was the 2014–2015 Ebola pandemic in West Africa, which infected approximately 28,610 individuals and approximately 11,300 lives were lost in Guinea, Liberia, and Sierra Leone. It is now widely recognized that a large-scale epidemic diffusion can conceivably cause many deaths and more people of permanent sequela, which presents a severe challenge to the local or regional health-care systems.


  1. 1.
    Henderson DA. The looming threat of bioterrorism. Science. 1999;283(5406):1279–82.CrossRefGoogle Scholar
  2. 2.
    Radosavljević V, Jakovljević B. Bioterrorism–types of epidemics, new epidemiological paradigm and levels of prevention. Public Health 2007;121(7):549–57.Google Scholar
  3. 3.
    Bouzianas DG. Medical countermeasures to protect humans from anthrax bioterrorism. Trends Microbiol. 2009;17(11):522–8.CrossRefGoogle Scholar
  4. 4.
    Wein LM, Craft DL, Kaplan EH. Emergency response to an anthrax attack. Proc Natl Acad Sci. 2003;100(7):4346–51.CrossRefGoogle Scholar
  5. 5.
    Wein LM, Liu Y, Leighton TJ. HEPA/vaccine plan for indoor anthrax remediation. Emerg Infect Dis. 2005;11(1):69–76.CrossRefGoogle Scholar
  6. 6.
    Craft DL, Wein LM, Wilkins AH. Analyzing bioterror response logistics: the case of anthrax. Manage Sci. 2005;51(5):679–94.CrossRefGoogle Scholar
  7. 7.
    Kaplan EH, Craft DL, Wein LM. Emergency response to a smallpox attack: the case for mass vaccination. Proc Natl Acad Sci. 2002;99(16):10935–40.CrossRefGoogle Scholar
  8. 8.
    Kaplan EH, Craft DL, Wein LM. Analyzing bioterror response logistics: the case of smallpox. Math Biosci. 2003;185(1):33–72.CrossRefGoogle Scholar
  9. 9.
    Mu YF, Shen LM. Modeling and implementation for flexible information system based on meta-data. Comput Eng. 2008;34(16):37–40.Google Scholar
  10. 10.
    Hiroyuki M, Kazuharu K, Nobuo N. Stochastic dynamics in biological system and information. Int J Innov Comput Inf Control. 2008;4(2):233–48.Google Scholar
  11. 11.
    Tadahiro K, Kenichi M, Nobuo N. The molecular dynamics calculation of clathrate hydrate structure stability for innovative organ preservation method. Int J Innov Comput, Inf Control. 2008;4(2):249–54.Google Scholar
  12. 12.
    Michael S, Hung KY, Chin LP. Constructing optimized bioinformatics parallel subtractor and divider with basic logic operations in the adleman-lipton model. ICIC Express Lett. 2009;3:1013–8.Google Scholar
  13. 13.
    Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’ networks. Nature. 1998;393:440–2.CrossRefGoogle Scholar
  14. 14.
    Eubank S, Guclu H, Anil Kumar VS, et al. Modelling disease outbreaks in realistic urban social networks. Nature (London). 2004;429(6988):180–4.CrossRefGoogle Scholar
  15. 15.
    Gama MM, Nunes A. Epidemics in small world networks. Eur Phys J B. 2006;50:205–8.CrossRefGoogle Scholar
  16. 16.
    Jari S, Kimmo K. Modeling development of epidemics with dynamic small-world networks. J Theor Biol. 2005;234(3):413–21.CrossRefGoogle Scholar
  17. 17.
    Masuda N, Konno N. Multi-state epidemic processes on complex networks. J Theor Biol. 2005;243(1):64–75.CrossRefGoogle Scholar
  18. 18.
    Xu XJ, Peng HO, Wang XM et al. Epidemic spreading with time delay in complex networks. Phys A Stat Mech Appl. 2005;367(C):525–30.Google Scholar
  19. 19.
    Han XP. Disease spreading with epidemic alert on small-world networks. Phys Lett A. 2007;365(1–2):1–5.CrossRefGoogle Scholar
  20. 20.
    Shi H, Duan Z, Chen G. An SIS model with infective medium on complex networks. Phys A. 2008;387(8–9):2133–44.CrossRefGoogle Scholar
  21. 21.
    Zhang H, Fu X. Spreading of epidemics on scale-free networks with nonlinear infectivity. Nonlinear Anal. 2009;70(9):3273–8.CrossRefGoogle Scholar
  22. 22.
    Liu M, Zhao LD. Optimization of the emergency materials distribution network with time windows in anti-bioterrorism system. Int J Innov Comput, Inf Control. 2009;5(11):3615–24.Google Scholar
  23. 23.
    Wang HY, Wang XP, Zeng AZ. Optimal material distribution decisions based on epidemic diffusion rule and stochastic latent period for emergency rescue. Int J Math Oper Res. 2009;1(1/2):76–96.CrossRefGoogle Scholar
  24. 24.
    Tham KY. An emergency department response to severe acute respiratory syndrome: a prototype response to bioterrorism. Ann Emerg Med. 2004;43(1):6–14.Google Scholar
  25. 25.
    Marco J, Dickman R. Nonequilibrium phase transitions in lattice models. Cambridge: Cambridge University Press; 1999.Google Scholar
  26. 26.
    Kermack WO, McKendrick AG. A contribution to the mathematical theory of epidemics. Proc Roy Soc London. Ser A. 1927;115(772):700–21. (Containing papers of a mathematical and physical character).Google Scholar
  27. 27.
    Coburn BJ, Wagner BG, Blower S. Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1). BMC Med. 2009;7(1):30–7.CrossRefGoogle Scholar
  28. 28.
    Dushoff J, Plotkin JB, Levin SA, et al. Dynamical resonance can account for seasonality of influenza epidemics. Proc Natl Acad Sci USA. 2004;101(48):16915–6.CrossRefGoogle Scholar
  29. 29.
    Stone L, Olinky R, Huppert A. Seasonal dynamics of recurrent epidemics. Nature (London). 2007;446(7135):533–6.CrossRefGoogle Scholar
  30. 30.
    Rvachev LA. Modeling experiment of a large-scale epidemic by means of a computer. Trans USSR Acad Sci Ser Math Phys. 1968;180:294–6.Google Scholar
  31. 31.
    Baroyan OV, Rvachev LA, Basilevsky UV, et al. Computer modelling of influenza epidemics for the whole country (USSR). Adv Appl Probab. 1971;3(2):224–6.CrossRefGoogle Scholar
  32. 32.
    Rvachev LA, Longini IM. A mathematical model for the global spread of inuenza. Math Biosci. 1985;75(1):3–22.CrossRefGoogle Scholar
  33. 33.
    Flahault A, Séverine D, Valleron AJ. A mathematical model for the european spread of influenza. Eur J Epidemiol. 1994;10(4):471–4.CrossRefGoogle Scholar
  34. 34.
    Caley P, Becker NG, Philp DJ. The waiting time for inter-country spread of pandemic influenza. PLOS ONE 2007;2:e143.
  35. 35.
    Viboud C. Synchrony, waves, and spatial hierarchies in the spread of influenza. Science (Washington DC). 2006;312(5772):447–51.CrossRefGoogle Scholar
  36. 36.
    Rachaniotis NP, Dasaklis TK, Pappis CP. A deterministic resource scheduling model in epidemic control: a case study. Eur J Oper Res. 2012;216(1):225–31.CrossRefGoogle Scholar
  37. 37.
    Gao Z, Kong D, Gao C. Modeling and control of complex dynamic systems: applied mathematical aspects. J Appl Math. 2012;2012(4):1–18.Google Scholar
  38. 38.
    Mishra B, Saini D. SEIRS epidemic model with delay for transmission of malicious objects in computer network. Appl Math Comput. 2007;188(2):1476–82.Google Scholar
  39. 39.
    Sun C, Hsieh YH. Global analysis of an SEIR model with varying population size and vaccination. Appl Math Model. 2010;34(10):2685–97.CrossRefGoogle Scholar
  40. 40.
    Li MY, Graef JR, Wang L, et al. Global dynamics of a SEIR model with varying total population size. Math Biosci. 1999;160(2):191–213.CrossRefGoogle Scholar
  41. 41.
    Zhang J, Li J, Ma Z. Global dynamics of an SEIR epidemic model with immigration of different compartments. Acta Math Sci. 2006;26(3):551–67.CrossRefGoogle Scholar
  42. 42.
    Zhang J, Ma Z. Global dynamics of an SEIR epidemic model with saturating contact rate. Math Biosci. 2003;185(1):15–32.CrossRefGoogle Scholar
  43. 43.
    Hethcote HW. Qualitative analyses of communicable disease models. Math Biosci. 1976;28(3–4):335–56.CrossRefGoogle Scholar
  44. 44.
    Kribs-Zaleta CM, Velasco-Hernández JX. A simple vaccination model with multiple endemic states. Math Biosci. 2000;164(2):183–201.Google Scholar
  45. 45.
    Liebovitch LS, Schwartz IB. Migration induced epidemics: dynamics of flux-based multipatch models. Phys Lett A. 2004;332(3–4):256–67.CrossRefGoogle Scholar
  46. 46.
    Sani A, Kroese DP. Controlling the number of HIV infectives in a mobile population. Math Biosci. 2008;213(2):103–12.CrossRefGoogle Scholar
  47. 47.
    Yang Y, Wu J, Li J, et al. Global dynamics–convergence to equilibria–of epidemic patch models with immigration. Math Comput Model. 2010;51(5–6):329–37.CrossRefGoogle Scholar
  48. 48.
    Wolkewitz M, Schumacher M. Simulating and analysing infectious disease data in a heterogeneous population with migration. Comput Methods Programs Biomed. 2011;104(2):29–36.CrossRefGoogle Scholar
  49. 49.
    Lee JM, Choi D, Cho G, et al. The effect of public health interventions on the spread of influenza among cities. J Theor Biol. 2012;293:131–42.CrossRefGoogle Scholar

Copyright information

© Science Press and Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.School of Economics and ManagementNanjing University of Science and TechnologyNanjingChina
  2. 2.Xuzhou University of TechnologyXuzhouChina
  3. 3.Nanjing Polytechnic InstituteNanjingChina
  4. 4.Affiliated Hospital of Jiangsu UniversityZhenjiangChina

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