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Modeling the spread of bed bug infestation and optimal resource allocation for disinfestation
1. | Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada |
References:
[1] |
L. J. S. Allen, F. Brauer, P. van den Driessche and J. Wu, Mathematical Epidemiology,, Springer-Verlag, (2008).
doi: 10.1007/978-3-540-78911-6. |
[2] |
C. Boase, Bedbugs-back from the brink,, Pestic. Outlook, 12 (2001), 159.
doi: 10.1039/b106301b. |
[3] |
C. Castillo-Chevez and H. R. Thieme, Asymptotically autonomous epidemic models,, Mathematical Population Dynamics: Analysis of Heterogeneity Vol. One: Theory of Epidemics, (1995), 33. Google Scholar |
[4] |
CBC News, Bedbug outbreaks hit Saint John, Sept. 22, 2010,, , (2015). Google Scholar |
[5] |
CBC News, Saint John hospital hit by bed bugs, Sept. 17, 2010,, , (2015). Google Scholar |
[6] |
S. L. Doggett and R. C. Russell, {Bed bugs-latest trends and developments,, Synopsis Aust. Environ. Pest Manag. Assoc. Natl. Conf., (2007), 22. Google Scholar |
[7] |
S. L. Doggett and A. E. P.t Managers Association, A Code of Practice for the Control of Bed Bug Infestations in Australia,, {Westmead Hospital, (2011). Google Scholar |
[8] |
S. L. Doggett, D. E. Dwyer, P. F. Peñas and R. C. Russell, Bed bugs: clinical relevance and control options,, Clin. Microbiol. Rev. 25 (2012), 25 (2012), 164.
doi: 10.1128/CMR.05015-11. |
[9] |
S. L. Doggett, M. J. Geary and R. C. Russell, The resurgence of bed bugs in Australia: With notes on their ecology and control,, Environmental Health, 4 (2004), 30. Google Scholar |
[10] |
S. L. Doggett, C. J. Orton, D. G. Lilly and R. C. Russell, {Bed bugs-a growing problem worldwide. Australian and international trends update and causes for concern,, Aust. Environ. Pest Manag. Assoc. NSW Conf. 2011, 2 (2011), 1. Google Scholar |
[11] |
S. L. Doggett and R. Russell, {Bed bugs: What the GP needs to know,, Aust. Fam. Physician, 38 (2009), 880. Google Scholar |
[12] |
S. L. Doggett and R. C. Russell, The resurgence of bed bugs, Cimex spp. (Hemiptera: Cimicidae) in Australia,, Proc. Sixth Int. Conf. Urban Pests, 6 (2008), 407. Google Scholar |
[13] |
P. Georgescu and G. Morosanu, Pest regulation by means of impulsive controls,, Appl. Math. Comput., 190 (2007), 790.
doi: 10.1016/j.amc.2007.01.079. |
[14] |
H. J. Harlan, Bed bugs 101: The basics of Cimex lectularius,, Am. Entomol., 52 (2006), 99. Google Scholar |
[15] |
S. W. Hwang, T. J. Svoboda, I. J. De Jong, K. J. Kabasele and E. Gogosis, Bed bug infestations in an urban environment,, Emerg. Infect. Dis., 11 (2005), 533.
doi: 10.3201/eid1104.041126. |
[16] |
L. Krueger, Features-don't get bitten by the resurgence of bed bugs-properly identifying a bed bug infestation is the key to quick control,, Pest Control, 68 (2000), 58. Google Scholar |
[17] |
Y. Kang and C. Castillo-Chavez, Dynamics of SI models with both horizontal and vertical transmissions as well as Allee effects,, Math. Biosci., 248 (2014), 97.
doi: 10.1016/j.mbs.2013.12.006. |
[18] |
M. P. Lehnert, R. M. Pereira, P. G. Koehler, W. Walker and M. S. Lehnert, Control of Cimex lectularius using heat combined with dichlorvos resin strips,, Med. Vet. Entomol., 25 (2011), 460. Google Scholar |
[19] |
S. M. Moghadas and A. B. Gumel, Global stability of a two-stage epidemic model with generalized non-linear incidence,, Math. Comput. Simulat., 60 (2002), 107.
doi: 10.1016/S0378-4754(02)00002-2. |
[20] |
R. K. McCormack and L. J. S. Allen, Disease emergence in multi-host epidemic models,, Mathematical Medicine and Biology, 24 (2007), 17. Google Scholar |
[21] |
D. J. Moore and D. M. Miller, Field evaluations of insecticide treatment regimens for control of the common bed bug, Cimex lectularius (L.),, Pest Manag. Sci., 65 (2009), 332. Google Scholar |
[22] |
J. D. Murray, Mathematical Biology I: An Introduction,, vol. 17 of Interdisciplinary Applied Mathematics, (2002).
|
[23] |
J. Paul and J. Bates, Is infestation with the common bedbug increasing,, BMJ, 320 (2000), 1141.
doi: 10.1136/bmj.320.7242.1141. |
[24] |
C. Paulhus and X.-S. Wang, Global stability analysis of a delayed susceptible-infected-susceptible epidemic model,, J. Biol. Dyn., 9 (2014), 45.
doi: 10.1080/17513758.2014.931474. |
[25] |
M. Pfiester, P. G. Koehler and R. M. Pereira, Effect of population structure and size on aggregation behavior of Cimex lectularius (Hemiptera: Cimicidae),, J. Med. Entomol., 46 (2009), 1015. Google Scholar |
[26] |
L. J. Pinto, R. Cooper and S. K. Kraft, Bed Bug Handbook: The Complete Guide to Bed Bugs and Their Control,, MD: Pinto & Associates, (2008). Google Scholar |
[27] |
K. Reinhardt and M. T. Siva-Jothy, Biology of the bed bugs (Cimicidae),, Annu. Rev. Entomol., 52 (2007), 351. Google Scholar |
[28] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems,, AMS Math. Surveys and Monographs, (1995).
|
[29] |
Statistics Canada, 2011 Census, , (). Google Scholar |
[30] |
H. Shu, D. Fan and J. Wei, Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission,, Nonlinear Anal. Real World Appl., 13 (2012), 1581.
doi: 10.1016/j.nonrwa.2011.11.016. |
[31] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.
doi: 10.1016/S0025-5564(02)00108-6. |
[32] |
E. L. Vargo, W. Booth, V. Saenz, R. G. Santangelo, C. Schal, W. H. Robinson and A. E. de Carvalho Campos, Genetic analysis of bed bug infestations and populations,, 7th Int. Conf. Urban Pests, 7 (2011), 319. Google Scholar |
[33] |
C. Wang and X. Wen, Bed bug infestations and control practices in China: Implications for fighting the global bed bug resurgence},, Insects, 2 (2011), 83.
doi: 10.3390/insects2020083. |
[34] |
L. Wang and B. Wood, An epidemiological approach to model the viral propagation of memes,, Appl. Math. Model., 35 (2011), 5442.
doi: 10.1016/j.apm.2011.04.035. |
[35] |
Z. Xiang, Y. Li and X. Song, Dynamic analysis of a pest management SEI model with saturation incidence concerning impulsive control strategy,, Nonlinear Anal. Real World Appl., 10 (2009), 2335.
doi: 10.1016/j.nonrwa.2008.04.017. |
[36] |
Z. Yuan and L. Wang, Global stability of epidemiological models with group mixing and nonlinear incidence rates,, Nonlinear Anal. Real World Appl., 11 (2010), 995.
doi: 10.1016/j.nonrwa.2009.01.040. |
[37] |
X.-Q. Zhao and Z.-J. Jing, Global asymptotic behavior in some cooperative systems of functional differential equations,, Canad. Appl. Math. Quart., 4 (1996), 421.
|
show all references
References:
[1] |
L. J. S. Allen, F. Brauer, P. van den Driessche and J. Wu, Mathematical Epidemiology,, Springer-Verlag, (2008).
doi: 10.1007/978-3-540-78911-6. |
[2] |
C. Boase, Bedbugs-back from the brink,, Pestic. Outlook, 12 (2001), 159.
doi: 10.1039/b106301b. |
[3] |
C. Castillo-Chevez and H. R. Thieme, Asymptotically autonomous epidemic models,, Mathematical Population Dynamics: Analysis of Heterogeneity Vol. One: Theory of Epidemics, (1995), 33. Google Scholar |
[4] |
CBC News, Bedbug outbreaks hit Saint John, Sept. 22, 2010,, , (2015). Google Scholar |
[5] |
CBC News, Saint John hospital hit by bed bugs, Sept. 17, 2010,, , (2015). Google Scholar |
[6] |
S. L. Doggett and R. C. Russell, {Bed bugs-latest trends and developments,, Synopsis Aust. Environ. Pest Manag. Assoc. Natl. Conf., (2007), 22. Google Scholar |
[7] |
S. L. Doggett and A. E. P.t Managers Association, A Code of Practice for the Control of Bed Bug Infestations in Australia,, {Westmead Hospital, (2011). Google Scholar |
[8] |
S. L. Doggett, D. E. Dwyer, P. F. Peñas and R. C. Russell, Bed bugs: clinical relevance and control options,, Clin. Microbiol. Rev. 25 (2012), 25 (2012), 164.
doi: 10.1128/CMR.05015-11. |
[9] |
S. L. Doggett, M. J. Geary and R. C. Russell, The resurgence of bed bugs in Australia: With notes on their ecology and control,, Environmental Health, 4 (2004), 30. Google Scholar |
[10] |
S. L. Doggett, C. J. Orton, D. G. Lilly and R. C. Russell, {Bed bugs-a growing problem worldwide. Australian and international trends update and causes for concern,, Aust. Environ. Pest Manag. Assoc. NSW Conf. 2011, 2 (2011), 1. Google Scholar |
[11] |
S. L. Doggett and R. Russell, {Bed bugs: What the GP needs to know,, Aust. Fam. Physician, 38 (2009), 880. Google Scholar |
[12] |
S. L. Doggett and R. C. Russell, The resurgence of bed bugs, Cimex spp. (Hemiptera: Cimicidae) in Australia,, Proc. Sixth Int. Conf. Urban Pests, 6 (2008), 407. Google Scholar |
[13] |
P. Georgescu and G. Morosanu, Pest regulation by means of impulsive controls,, Appl. Math. Comput., 190 (2007), 790.
doi: 10.1016/j.amc.2007.01.079. |
[14] |
H. J. Harlan, Bed bugs 101: The basics of Cimex lectularius,, Am. Entomol., 52 (2006), 99. Google Scholar |
[15] |
S. W. Hwang, T. J. Svoboda, I. J. De Jong, K. J. Kabasele and E. Gogosis, Bed bug infestations in an urban environment,, Emerg. Infect. Dis., 11 (2005), 533.
doi: 10.3201/eid1104.041126. |
[16] |
L. Krueger, Features-don't get bitten by the resurgence of bed bugs-properly identifying a bed bug infestation is the key to quick control,, Pest Control, 68 (2000), 58. Google Scholar |
[17] |
Y. Kang and C. Castillo-Chavez, Dynamics of SI models with both horizontal and vertical transmissions as well as Allee effects,, Math. Biosci., 248 (2014), 97.
doi: 10.1016/j.mbs.2013.12.006. |
[18] |
M. P. Lehnert, R. M. Pereira, P. G. Koehler, W. Walker and M. S. Lehnert, Control of Cimex lectularius using heat combined with dichlorvos resin strips,, Med. Vet. Entomol., 25 (2011), 460. Google Scholar |
[19] |
S. M. Moghadas and A. B. Gumel, Global stability of a two-stage epidemic model with generalized non-linear incidence,, Math. Comput. Simulat., 60 (2002), 107.
doi: 10.1016/S0378-4754(02)00002-2. |
[20] |
R. K. McCormack and L. J. S. Allen, Disease emergence in multi-host epidemic models,, Mathematical Medicine and Biology, 24 (2007), 17. Google Scholar |
[21] |
D. J. Moore and D. M. Miller, Field evaluations of insecticide treatment regimens for control of the common bed bug, Cimex lectularius (L.),, Pest Manag. Sci., 65 (2009), 332. Google Scholar |
[22] |
J. D. Murray, Mathematical Biology I: An Introduction,, vol. 17 of Interdisciplinary Applied Mathematics, (2002).
|
[23] |
J. Paul and J. Bates, Is infestation with the common bedbug increasing,, BMJ, 320 (2000), 1141.
doi: 10.1136/bmj.320.7242.1141. |
[24] |
C. Paulhus and X.-S. Wang, Global stability analysis of a delayed susceptible-infected-susceptible epidemic model,, J. Biol. Dyn., 9 (2014), 45.
doi: 10.1080/17513758.2014.931474. |
[25] |
M. Pfiester, P. G. Koehler and R. M. Pereira, Effect of population structure and size on aggregation behavior of Cimex lectularius (Hemiptera: Cimicidae),, J. Med. Entomol., 46 (2009), 1015. Google Scholar |
[26] |
L. J. Pinto, R. Cooper and S. K. Kraft, Bed Bug Handbook: The Complete Guide to Bed Bugs and Their Control,, MD: Pinto & Associates, (2008). Google Scholar |
[27] |
K. Reinhardt and M. T. Siva-Jothy, Biology of the bed bugs (Cimicidae),, Annu. Rev. Entomol., 52 (2007), 351. Google Scholar |
[28] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems,, AMS Math. Surveys and Monographs, (1995).
|
[29] |
Statistics Canada, 2011 Census, , (). Google Scholar |
[30] |
H. Shu, D. Fan and J. Wei, Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission,, Nonlinear Anal. Real World Appl., 13 (2012), 1581.
doi: 10.1016/j.nonrwa.2011.11.016. |
[31] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.
doi: 10.1016/S0025-5564(02)00108-6. |
[32] |
E. L. Vargo, W. Booth, V. Saenz, R. G. Santangelo, C. Schal, W. H. Robinson and A. E. de Carvalho Campos, Genetic analysis of bed bug infestations and populations,, 7th Int. Conf. Urban Pests, 7 (2011), 319. Google Scholar |
[33] |
C. Wang and X. Wen, Bed bug infestations and control practices in China: Implications for fighting the global bed bug resurgence},, Insects, 2 (2011), 83.
doi: 10.3390/insects2020083. |
[34] |
L. Wang and B. Wood, An epidemiological approach to model the viral propagation of memes,, Appl. Math. Model., 35 (2011), 5442.
doi: 10.1016/j.apm.2011.04.035. |
[35] |
Z. Xiang, Y. Li and X. Song, Dynamic analysis of a pest management SEI model with saturation incidence concerning impulsive control strategy,, Nonlinear Anal. Real World Appl., 10 (2009), 2335.
doi: 10.1016/j.nonrwa.2008.04.017. |
[36] |
Z. Yuan and L. Wang, Global stability of epidemiological models with group mixing and nonlinear incidence rates,, Nonlinear Anal. Real World Appl., 11 (2010), 995.
doi: 10.1016/j.nonrwa.2009.01.040. |
[37] |
X.-Q. Zhao and Z.-J. Jing, Global asymptotic behavior in some cooperative systems of functional differential equations,, Canad. Appl. Math. Quart., 4 (1996), 421.
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