An Epidemic Patchy Model with Entry–Exit Screening

Bulletin of Mathematical Biology

Volumn 77, Issue 7, 2015, Pages 1237-1255

  Wang, Xinxin ^a   Liu, Shengqiang ^a   Wang, Lin ^b   Zhang, Weiwei ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF NEW BRUNSWICK   (Canada)

Author keywords

Dispersal; Entry exit screening; Epidemic model; Patchy environment; Threshold dynamics

Indexed keywords

BASIC REPRODUCTION NUMBER; BIOLOGICAL MODEL; COMMUNICABLE DISEASES; EPIDEMICS; HUMAN; INFLUENZA A VIRUS (H1N1); INFLUENZA, HUMAN; MASS SCREENING; MATHEMATICAL PHENOMENA; PANDEMICS; STATISTICS AND NUMERICAL DATA; TRANSMISSION; TRAVEL;

BASIC REPRODUCTION NUMBER; COMMUNICABLE DISEASES; EPIDEMICS; HUMANS; INFLUENZA A VIRUS, H1N1 SUBTYPE; INFLUENZA, HUMAN; MASS SCREENING; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; PANDEMICS; TRAVEL;

EID: 84940450499     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-015-0084-6     Document Type: Article

References (56)

1. Ainseba B, Iannelli M (2012) Optimal screening in structured SIR epidemics. Math Model Nat Phenom 7(03):12–27
2. Allen L, Bolker B, Lou Y, Nevai A (2007) Asymptotic profiles of the steady states for an sis epidemic patch model. SIAM J Appl Math 67(5):1283–1309
3. Alonso D, McKane A (2002) Extinction dynamics in mainland-island metapopulations: an N-patch stochastic model. Bull Math Biol 64(5):913–958
4. Arino J, Davis JR, Hartley D, Jordan R, Miller JM, van den Driessche P (2005) A multi-species epidemic model with spatial dynamics. Math Med Biol 22(2):129–142
5. Arino J, van den Driessche P (2003a) A multi-city epidemic model. Math Popul Stud 10(3):175–193
6. Arino J, van den Driessche P (2003b) The basic reproduction number in a multi-city compartmental epidemic model. In: Benvenuti L, De Santis A, Farina L (eds) Positive systems, Springer, Berlin, Heidelberg, pp 135–142
7. Arino J, van den Driessche P (2006) Disease spread in metapopulations. Nonlinear Dyn Evol Equ Fields Inst Commun 48:1–13
8. Bauch C, Rand D (2000) A moment closure model for sexually transmitted disease transmission through a concurrent partnership network. Proc R Soc Lond Ser B Biol Sci 267(1456):2019–2027
9. Blower SM, Dowlatabadi H (1994) Sensitivity and uncertainty analysis of complexmodels of disease transmission: an HIV model as an example. Int Stat Rev 62:229–243
10. Bolker BM (1999) Analytic models for the patchy spread of plant disease. Bul Math Biol 615:849–874
11. Brauer F, van den Driessche P (2001) Models for transmission of disease with immigration of infectives. Math Biosci 171(2):143–154
12. Brauer F, van den Driessche P, Wang L (2008) Oscillations in a patchy environment disease model. Math Biosci 215(1):1–10
13. Brown DH, Bolker BM (2004) The effects of disease dispersal and host clustering on the epidemic threshold in plants. Bull Math Biol 66(2):341–371
14. Clancy D, Pearce CJ (2013) The effect of population heterogeneities upon spread of infection. J Math Biol 67(4):963–987
15. Cowling B et al (2010) Entry screening to delay local transmission of 2009 pandemic influenza A (H1N1). BMC Infect Dis 10:82
16. Eisenberg MC, Shuai Z, Tien JH, van den Driessche P (2013) A cholera model in a patchy environment with water and human movement. Math Biosci 246(1):105–112
17. Feng Z (2007) Final and peak epidemic sizes for SEIR models with quarantine and isolation. Math Biosci Eng 4(4):675–686
18. Gao D, Ruan S (2013) Modeling the spatial spread of Rift Valley fever in Egypt. Bull Math Biol 75:523–542
19. Gao R, Cao B, Hu Y, Feng Z, Wang D, Hu W, Chen J, Jie Z, Qiu H, Xu K et al (2013) Human infection with a novel avian-origin influenza A(H7N9) virus. N Engl J Med 368(20):1888–1897
20. Gerberry D, Milner F (2009) An SEIQR model for childhood diseases. J Math Biol 59:535–561
21. Gumel AB, Ruan SG, Day T et al (2004) Modelling strategies for controlling SARS outbreaks. Proc R Soc Lond B 271:2223–2232
22. Hethcote HW (1976) Qualitative analyses of communicable disease models. Math Biosci 28(3):335–356
23. Hethcote HW, Ma Z, Liao S (2002) Effects of quarantine in six endemic models for infectious diseases. Math Biosci 180:141–160
24. Hirsch MW, Smith HL, Zhao XQ (2001) Chain transitivity, attractivity, and strong repellors for semidynamical systems. J Dyn Differ Equ 13(1):107–131
25. Hsieh YH, van den Driessche P, Wang L (2007) Impact of travel between patches for spatial spread of disease. Bull Math Biol 69(4):1355–1375
26. Hsu SB, Hsieh YH (2005) Modeling intervention measures and severity-dependent public response during severe acute respiratory syndrome outbreak. SIAM J Appl Math 66(2):627–647
27. Hove-Musekwa SD, Nyabadza F (2009) The dynamics of an HIV/AIDS model with screened disease carriers. Comput Math Methods Med 10(4):287–305
28. Hyman JM, Li J, Stanley E (2003) Modeling the impact of random screening and contact tracing in reducing the spread of HIV. Math Biosci 181(1):17–54
29. Jones KE, Patel NG, Levy MA, Storeygard A, Balk D, Gittleman JL, Daszak P (2008) Global trends in emerging infectious diseases. Nature 451(7181):990–993
30. Khan K, Eckhardt R, Brownstein JS, Naqvi R, Hu W, Kossowsky D, Scales D, Arino J, MacDonald M, Wang J et al (2013) Entry and exit screening of airline travellers during the A(H1N1) 2009 pandemic: a retrospective evaluation. Bull World Health Organ 91(5):368–376
31. Li JY, Cui B, Wang L, Chen CT, Ci Y, Guo WJ (2013) The effect of strengthening the frontier health quarantine to prevent and control the epidemic of influenza A (H1N1) from abroad. J Insp Quar (Chin) 23(2):56–58
32. Lipsitch M, Cohen T, Cooper B, Robins JM, Ma S, James L, Gopalakrishna G, Chew SK, Tan CC, Samore MH et al (2003) Transmission dynamics and control of severe acute respiratory syndrome. Science 300(5627):1966–1970
33. Liu XN, Chen X, Takeuchi Y (2011) Dynamics of an SIQS epidemic model with transport-related infection and exit–entry screenings. J Theor Biol 285(1):25–35
34. Liu XN, Takeuchi Y (2006) Spread of disease with transport-related infection and entry screening. J Theor Biol 242(2):517–528
35. Liu XZ, Stechlinski P (2013) Transmission dynamics of a switched multi-city model with transport-related infections. Nonlinear Anal Real World Appl 14(1):264–279
36. Nyabadza F, Mukandavire Z (2011) Modelling HIV/AIDS in the presence of an A(H1N1) testing and screening campaign. J Theor Biol 280(1):167–179
37. Perko L (2001) Differential equations and dynamical systems. Springer, New York
38. Ruan S, Wang W, Levin SA et al (2006) The effect of global travel on the spread of SARS. Math Biosci Eng 3(1):205–218
39. Safi M, Gumel A (2010) Global asymptotic dynamics of a model for quarantine and isolation. Discrete Contin Dyn Syst Ser B 14:209–231
40. Sattenspiel L, Herring DA (2003) Simulating the effect of quarantine on the spread of the 1918–19 flu in central Canada. Bull Math Biol 65(1):1–26
41. Smith GJ, Vijaykrishna D, Bahl J, Lycett SJ, Worobey M, Pybus OG, Ma SK, Cheung CL, Raghwani J, Bhatt S et al (2009) Origins and evolutionary genomics of the 2009 swine-origin H1N1 influenza a epidemic. Nature 459(7250):1122–1125
42. Smith HL (1995) The theory of the chemostat: dynamics of microbial competition, vol 13. Cambridge University Press, Cambridge
43. Smith HL (2008) Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, vol 41. American Mathematical Society, Providence
44. Tang S, Chen L (2002) Density-dependent birth rate, birth pulses and their population dynamic consequences. J Math Biol 44(2):185–199
45. Tang S, Xiao Y, Yang Y, Zhou Y, Wu J, Ma Z et al (2010) Community-based measures for mitigating the 2009 H1N1 pandemic in China. PLoS One 5(6):e10911
46. Tang SY, Xiao YN, Yuan L, Cheke RA, Wu JH (2012) Campus quarantine (Fengxiao) for curbing emergent infectious diseases: lessons from mitigating A/H1N1 in Xi’an, China. J Theor Biol 295(4):47–58
47. van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180(1):29–48
48. Wang L, Wang X (2012) Influence of temporary migration on the transmission of infectious diseases in a migrants’ home village. J Theor Biol 300:100–109
49. Wang W, Zhao XQ (2004) An epidemic model in a patchy environment. Math Biosci 190(1):97–112
50. Wu J, Dhingra R, Gambhir M, Remais JV (2013) Sensitivity analysis of infectious disease models: methods, advances and their application. J R Soc Interface 10:20121018
51. Xiao YN, Tang SY, Wu JH (2015) Media impact switching surface during an infectious disease outbreak. Sci Rep 5:7838. doi:10.1038/srep07838
52. Xu CL, Sun SH et al (2011) Epidemiological characteristics of confirmed cases of pandemic influenza A (H1N1) 2009 in mainland China, 2009–2010. Dis Surveill 26:780–784
53. Yu H, Cauchemez S, Donnelly CA, Zhou L, Feng L, Xiang N, Zheng J, Ye M, Huai Y, Liao Q et al (2012) Transmission dynamics, border entry screening, and school holidays during the 2009 influenza A (H1N1) pandemic, China. Emerg Infect Dis 18(5):758
54. Yu H, Liao Q, Yuan Y, Zhou L, Xiang N, Huai Y, Guo X, Zheng Y, van Doorn HR, Farrar J et al (2010) Effectiveness of oseltamivir on disease progression and viral rna shedding in patients with mild pandemic 2009 influenza A H1N1: opportunistic retrospective study of medical charts in China. Br Med J 341:c4779. doi:10.1136/bmj.c4779
55. Zhao XQ (1995) Uniform persistence and periodic coexistence states in infinite-dimensional periodic semiflows with applications. Can Appl Math Q 3:473–495
56. Zhao XQ, Jing ZJ (1996) Global asymptotic behavior in some cooperative systems of functional differential equations. Can Appl Math Q 4(4):421–444