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Hopf Bifurcation in An Epidemic Model of a Vector-Borne Disease with Time Delay

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Author:: No author available

Journal Title:: Journal of Biomathematics

Issue:: 4

DOI:: No doi available

Key Word:: 流行模型;平衡分析;稳定性;阈值;Hopt分支;Epidemic models;Equilibrium analysis;Stability;Threshold;Hopfbifurcation

Abstract： This paper considers an epidemic model of a vector-borne disease with delay.The incidence term is assumed to be of the bilinear mass-action form.The model shows that the dynamics is determined by the basic reproduction number R0.If R0 ≤ 1,the disease-free equilibrium is globally stable and the disease dies out.If R0 ＞ 1,a unique endemic equilibrium exists in the interior of the feasible region.The delay in the differential-delay model accounts for the incubation time the vectors need to become infectious.We study the effect of that delay on the stability of the equilibria.We show that the introduction of a time delay in the host-to-vector transmission term can destabilize the system and periodic solutions can arise through Hopf bifurcation.

Reference

[1]Sutherst RW.Global change and human vulnerability to vector-borne diseases.[J].2004,17(1).
[2]Esteva L,Vargas C.A model for dengue disease with variable human population.[J].1999,38(3).
[3]Robert T.Watson,Jonathan Patz,Duane J.Gubler,etc.Environmental health implications of global climate change[J].2005,7(9).
[4]C, Bowman,A B, Gumel,P, van den Driessche,etc.A mathematical model for assessing control strategies against West Nile virus.[J].2005,67(5).
[5]Porco, T. C..A mathematical model of the ecology of Lyme disease[J].1999,16(3).
[6]Vargas C.,Esteva L..Analysis of a Dengue disease transmission model[J].1998,150(2).
[7]Khasnis AA,Nettleman MD.Global warming and infectious disease.[J].2005,36(6).
[8]Esteva L.,Vargas C..Influence of vertical and mechanical transmission on the dynamics of dengue disease[J].2000,167(1).
[9]Mwambi, H. G..Ticks and tick-borne diseases in Africa: a disease transmission model[J].2002,19(4).
[10]Boots M,Kawaguchi I,Sasaki A.Why are dengue virus serotypes so distantly related? Enhancement and limiting serotype similarity between dengue virus strains.[J].2003,270(1530).
[11]Mini, Ghosh,Andrea, Pugliese.Seasonal population dynamics of ticks, and its influence on infection transmission: a semi-discrete approach.[J].2004,66(6).
[12]P, Pongsumpun,I M, Tang.A realistic age structured transmission model for dengue hemorrhagic fever in Thailand.[J].2001,32(2).
[13]Gubler, Duane J..Resurgent vector-borne diseases as a global health problem.[J].1998,4(3).
[14]D H, Molyneux.Patterns of change in vector-borne diseases.[J].1997,91(7).
[15]Esteva L.,Vargas C..Coexistence of different serotypes of dengue virus[J].2003,46(1).
[16]Neil M. Ferguson,Roy M. Anderson,Christl A. Donnelly.Transmission dynamics and epidemiology of dengue: insights from age-stratified sero-prevalence surveys[J].1999,354(1384).
[17]Rosa R,Pugliese A,Norman R,etc.Thresholds for disease persistence in models for tick-borne infections including non-viraemic transmission, extended feeding and tick aggregation.[J].2003,224(3).
[18]Nobuhiko Nagai,Setsuo Suguri,Akira Ishii,etc.A mathematical model for the transmission of Plasmodium vivax malaria[J].2003,52(1).
[19]Esteva L,Yang HM.Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique[J].2005,198(2).
[20]Feng ZL.,Velascohernandez JX..Competitive Exclusion in a Vector-Host Model for the Dengue Fever[J].1997,35(5).
[21]Gardner G.,Szymanski BK.,Maniatty W.,etc.Lyme disease: Self-regulation and pathogen invasion[J].1998,193(4).
[22]Harrus, S.,Baneth, G..Drivers for the emergence and re-emergence of vector-borne protozoal and bacterial diseases[J].2005,35(11).
[23]Shrivastava R,Nagar R,Chaturvedi UC.Dengue vaccines: problems and prospects.[J].2005,121(5).
[24]D J, Rodríguez,L, Torres-Sorando.Models of infectious diseases in spatially heterogeneous environments.[J].2001,63(3).
[25]Sekine H,Inaba H.A mathematical model for Chagas disease with infection-age-dependent infectivity[J].2004,190(1).
[26]E A, Newton,P, Reiter.A model of the transmission of dengue fever with an evaluation of the impact of ultra-low volume (ULV) insecticide applications on dengue epidemics.[J].1992,47(6).
[27]J C, Koella,R, Antia.Epidemiological models for the spread of anti-malarial resistance.[J].2003,2.
[28]Cologna R,Rico-Hesse R,Armstrong PM.Selection for virulent dengue viruses occurs in humans and mosquitoes[J].2005,79(2).
[29]Charles H, Calisher.Persistent emergence of dengue.[J].2005,11(5).
[30]Takeuchi Y.,Beretta E.,Ma WB..Global asymptotic properties of a delay SIR epidemic model with finite incubation times[J].2000,42(6).
[31]D J, Rogers.The dynamics of vector-transmitted diseases in human communities.[J].1988,321(1207).
[32]Lucy Tiemi Takahashi,Norberto Anibal Maidana,Wilson Castro Ferreira,etc.Mathematical models for the Aedes aegypti dispersal dynamics: Travelling waves by wing and wind[J].2005,67(3).
[33]Mackinnon MJ.Drug resistance models for malaria.[J].2005,94(3).
[34]Feng ZL,Smith DL,McKenzie FE,etc.Coupling ecology and evolution: malaria and the S-gene across time scales[J].2004,189(1).
[35]Boete C.,Koella JC..A model for the coevolution of immunity and immune evasion in Vector-Borne diseases with implications for the epidemiology of malaria[J].2003,161(5).
[36]Ferguson N,Anderson R,Gupta S.The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens.[J].1999,96(2).
[37]M, Derouich,A, Boutayeb,E H, Twizell.A model of dengue fever.[J].2003,2.