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What can mathematical models tell us about the relationship between circular migrations and HIV transmission dynamics?
Dynamics of evolutionary competition between budding and lytic viral release strategies
1.  Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada 
2.  Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7 
References:
[1] 
A. Brännstr$\ddot o$m and D. J. T. Sumpter, The role of competition and clustering in population dynamics, Proc. R. Soc. B., 272 (2005), 20652072. 
[2] 
J. Carter and V. Saunders, Virology: Principles and Application, John Wiley and Sons, Ltd, 2007. 
[3] 
C. CastilloChaves and H. R. Thieme, Asymptotically autonomous epidemic models, in Mathematical Population Dynamics: Analysis of Heterogeneity, I. Theory of Epidemics (eds. O. Arino, et al.), Wuerz, Winnnipeg, 1995, 3350. 
[4] 
D. Coombs, Optimal viral production, Bull. Math. Biol., 65 (2003), 10031023. doi: 10.1016/S00928240(03)000569. 
[5] 
H. Garoff, R. Hewson and D. Opstelten, Virus maturation by budding, Microbiology and Moleculer Biology Reviews, 62 (1998), 11711190. 
[6] 
M. A. Gilchrist, D. Coombs and A. S. Perelson, Optimizing withinhost viral fitness: Infected cell lifespan and virion production rate, J. Theor. Biol. 229 (2004), 281288. doi: 10.1016/j.jtbi.2004.04.015. 
[7] 
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, SpringerVerlag, New York, 1993. doi: 10.1007/9781461243427. 
[8] 
N. L. Komarova, Viral reproductive strategies: How can lytic viruses be evolutionarily competitive? J. Theor. Biol., 249 (2007), 766784. doi: 10.1016/j.jtbi.2007.09.013. 
[9] 
D. P. Nayak, Assembly and budding of influenza virus, Virus Research, 106 (2004), 147165. doi: 10.1016/j.virusres.2004.08.012. 
[10] 
P. W. Nelson, M. A. Gilchrist, D. Coombs, J. M. Hyman and A. S. Perelson, An agestructured model of HIV infection that allows for variation in the production rate of viral particles and the death rate of productively infected cells, Math. Biosci. Eng., 1 (2004), 267288. doi: 10.3934/mbe.2004.1.267. 
[11] 
L. Rong, Z. Feng and A. S. Perelson, Mathematical analysis of agestructured HIV1 dynamics with combination antiretroviral therapy, J. Appl. Math., 67 (2007), 731756. doi: 10.1137/060663945. 
[12] 
H. L. Smith, Monotone Dynamical Systems. An Introduction To The Theory Of Competitive And Cooperative Systems, Mathematical Surveys and Monographs, 41, AMS, Providence, 1995. 
[13] 
I. N. Wang, D. E. Dykhuizen and L. B. Slobodkin, The evolution of phage lysis timing, Evolutionary Ecology, 10 (1996), 545558. doi: 10.1007/BF01237884. 
[14] 
I. N. Wang, Lysis timing and bacteriophage fitness, Genetics, 172 (2006), 1726. doi: 10.1534/genetics.105.045922. 
show all references
References:
[1] 
A. Brännstr$\ddot o$m and D. J. T. Sumpter, The role of competition and clustering in population dynamics, Proc. R. Soc. B., 272 (2005), 20652072. 
[2] 
J. Carter and V. Saunders, Virology: Principles and Application, John Wiley and Sons, Ltd, 2007. 
[3] 
C. CastilloChaves and H. R. Thieme, Asymptotically autonomous epidemic models, in Mathematical Population Dynamics: Analysis of Heterogeneity, I. Theory of Epidemics (eds. O. Arino, et al.), Wuerz, Winnnipeg, 1995, 3350. 
[4] 
D. Coombs, Optimal viral production, Bull. Math. Biol., 65 (2003), 10031023. doi: 10.1016/S00928240(03)000569. 
[5] 
H. Garoff, R. Hewson and D. Opstelten, Virus maturation by budding, Microbiology and Moleculer Biology Reviews, 62 (1998), 11711190. 
[6] 
M. A. Gilchrist, D. Coombs and A. S. Perelson, Optimizing withinhost viral fitness: Infected cell lifespan and virion production rate, J. Theor. Biol. 229 (2004), 281288. doi: 10.1016/j.jtbi.2004.04.015. 
[7] 
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, SpringerVerlag, New York, 1993. doi: 10.1007/9781461243427. 
[8] 
N. L. Komarova, Viral reproductive strategies: How can lytic viruses be evolutionarily competitive? J. Theor. Biol., 249 (2007), 766784. doi: 10.1016/j.jtbi.2007.09.013. 
[9] 
D. P. Nayak, Assembly and budding of influenza virus, Virus Research, 106 (2004), 147165. doi: 10.1016/j.virusres.2004.08.012. 
[10] 
P. W. Nelson, M. A. Gilchrist, D. Coombs, J. M. Hyman and A. S. Perelson, An agestructured model of HIV infection that allows for variation in the production rate of viral particles and the death rate of productively infected cells, Math. Biosci. Eng., 1 (2004), 267288. doi: 10.3934/mbe.2004.1.267. 
[11] 
L. Rong, Z. Feng and A. S. Perelson, Mathematical analysis of agestructured HIV1 dynamics with combination antiretroviral therapy, J. Appl. Math., 67 (2007), 731756. doi: 10.1137/060663945. 
[12] 
H. L. Smith, Monotone Dynamical Systems. An Introduction To The Theory Of Competitive And Cooperative Systems, Mathematical Surveys and Monographs, 41, AMS, Providence, 1995. 
[13] 
I. N. Wang, D. E. Dykhuizen and L. B. Slobodkin, The evolution of phage lysis timing, Evolutionary Ecology, 10 (1996), 545558. doi: 10.1007/BF01237884. 
[14] 
I. N. Wang, Lysis timing and bacteriophage fitness, Genetics, 172 (2006), 1726. doi: 10.1534/genetics.105.045922. 
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