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Finite element approximation of a population spatial adaptation model
Identifying requirements for the invasion of a tick species and tickborne pathogen through TICKSIM
1.  Department of Biological Sciences, Old Dominion University, 110 MGB, Norfolk, Virginia 23529, United States, United States 
References:
[1] 
B. E. Anderson, K. G. Sims, J. G. Olson, J. E. Childs and J. F. Piesman, Amblyomma americanum: A potential vector of human ehrlichiosis,, American Journal of Tropical Medicine and Hygiene, 49 (1993), 239. 
[2] 
Centers for Disease Control and Prevention, Summary of notifiable diseases  United States, 2006,, MMWR, 55 (2008), 1. 
[3] 
J. E. Childs and C. D. Paddock, The ascendancy of Amblyomma americanum as a vector of pathogens affecting humans in the United States,, Annual Review of Entomology, 48 (2003), 307. 
[4] 
F. S. Dahlgren, E. J. Mandel, J. W. Krebs, R. F. Massung and J. H. McQuiston, Increasing Incidence of Ehrlichia chaffeensis and Anaplasma phagocytophilum in the United States, 20002007,, American Journal of Tropical Medicine and Hygiene, 85 (2011), 124. 
[5] 
S. A. Ewing, J. E. Dawson, A. A. Kocan, R. W. Barker, C. K. Warner, R. J. Panciera, J. C. Fox, K. M. Kocan and E. F. Bouin, Experimental transmission of Ehrlichia chaffeensis (Rickettsiales: Ehrlichieae) among whitetailed deer by Amblyomma americanum(Acari: Ixodidae),, Journal of Medical Entomology, 32 (1995), 368. 
[6] 
D. B. Fishbein, J. E. Dawson and L. E. Robinson, Human ehrlichiosis in the United States, 1985 to 1990,, Annals of Internal Medicine, 120 (1994), 736. 
[7] 
H. D. Gaff, Preliminary analysis of an agent based model for a tickborne disease,, Mathematical Biosciences and Engineering, 8 (2011), 463. doi: 10.3934/mbe.2011.8.463. 
[8] 
V. Grimm, U. Berger, D. L. DeAngelis, J. G. Polhill, J. Giske and S. F. Railsback, The ODD protocol: A review and first update,, Ecological Modelling, 221 (2010), 2760. doi: 10.1016/j.ecolmodel.2010.08.019. 
[9] 
J. Goodman, D. Dennis and D. Sonenshine, Tick borne diseases of humans,, American Society of Microbiology, (2005). doi: 10.1086/504876. 
[10] 
H. A. Merten and L. A. Durden, A statebystate survey of ticks recorded from humans in the United States,, Journal of Vector Ecology, 25 (2000), 102. 
[11] 
C. D. Paddock and J. E. Childs, Ehrlichia chaffeensis: A prototypical emerging pathogen,, Clinical Microbiology Reviews, 16 (2003), 37. 
[12] 
C. D. Paddock and M. J. Yabsley, Ecological havoc, the rise of whitetailed deer, and the emergence of Amblyomma americanumassociated zoonoses in the United States,, Current Topics in Microbiology and Immunology, 315 (2007), 289. 
[13] 
C. D. Patrick and J. A. Hair, Whitetailed deer utilization of different habitats and its influence on lone star tick population,, Journal of Parasitology, 64 (1978), 1100. doi: 10.2307/3279735. 
[14] 
E. Y. Stromdahl, M. P. Randolph, J. J. O'Brien, and A. G. Gutierrez, Ehrlichia chaffeensis (Rickettsiales: Ehrlichieae) infection in Amblyomma americanum (Acari: Ixodidae) at Aberdeen Proving Ground, Maryland,, Journal of Medical Entomology, 37 (2000), 349. 
show all references
References:
[1] 
B. E. Anderson, K. G. Sims, J. G. Olson, J. E. Childs and J. F. Piesman, Amblyomma americanum: A potential vector of human ehrlichiosis,, American Journal of Tropical Medicine and Hygiene, 49 (1993), 239. 
[2] 
Centers for Disease Control and Prevention, Summary of notifiable diseases  United States, 2006,, MMWR, 55 (2008), 1. 
[3] 
J. E. Childs and C. D. Paddock, The ascendancy of Amblyomma americanum as a vector of pathogens affecting humans in the United States,, Annual Review of Entomology, 48 (2003), 307. 
[4] 
F. S. Dahlgren, E. J. Mandel, J. W. Krebs, R. F. Massung and J. H. McQuiston, Increasing Incidence of Ehrlichia chaffeensis and Anaplasma phagocytophilum in the United States, 20002007,, American Journal of Tropical Medicine and Hygiene, 85 (2011), 124. 
[5] 
S. A. Ewing, J. E. Dawson, A. A. Kocan, R. W. Barker, C. K. Warner, R. J. Panciera, J. C. Fox, K. M. Kocan and E. F. Bouin, Experimental transmission of Ehrlichia chaffeensis (Rickettsiales: Ehrlichieae) among whitetailed deer by Amblyomma americanum(Acari: Ixodidae),, Journal of Medical Entomology, 32 (1995), 368. 
[6] 
D. B. Fishbein, J. E. Dawson and L. E. Robinson, Human ehrlichiosis in the United States, 1985 to 1990,, Annals of Internal Medicine, 120 (1994), 736. 
[7] 
H. D. Gaff, Preliminary analysis of an agent based model for a tickborne disease,, Mathematical Biosciences and Engineering, 8 (2011), 463. doi: 10.3934/mbe.2011.8.463. 
[8] 
V. Grimm, U. Berger, D. L. DeAngelis, J. G. Polhill, J. Giske and S. F. Railsback, The ODD protocol: A review and first update,, Ecological Modelling, 221 (2010), 2760. doi: 10.1016/j.ecolmodel.2010.08.019. 
[9] 
J. Goodman, D. Dennis and D. Sonenshine, Tick borne diseases of humans,, American Society of Microbiology, (2005). doi: 10.1086/504876. 
[10] 
H. A. Merten and L. A. Durden, A statebystate survey of ticks recorded from humans in the United States,, Journal of Vector Ecology, 25 (2000), 102. 
[11] 
C. D. Paddock and J. E. Childs, Ehrlichia chaffeensis: A prototypical emerging pathogen,, Clinical Microbiology Reviews, 16 (2003), 37. 
[12] 
C. D. Paddock and M. J. Yabsley, Ecological havoc, the rise of whitetailed deer, and the emergence of Amblyomma americanumassociated zoonoses in the United States,, Current Topics in Microbiology and Immunology, 315 (2007), 289. 
[13] 
C. D. Patrick and J. A. Hair, Whitetailed deer utilization of different habitats and its influence on lone star tick population,, Journal of Parasitology, 64 (1978), 1100. doi: 10.2307/3279735. 
[14] 
E. Y. Stromdahl, M. P. Randolph, J. J. O'Brien, and A. G. Gutierrez, Ehrlichia chaffeensis (Rickettsiales: Ehrlichieae) infection in Amblyomma americanum (Acari: Ixodidae) at Aberdeen Proving Ground, Maryland,, Journal of Medical Entomology, 37 (2000), 349. 
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