Repulsion Effect on Superinfecting Virions by Infected Cells

Bulletin of Mathematical Biology

Volumn 76, Issue 11, 2014, Pages 2806-2833

  Lai, Xiulan ^a   Zou, Xingfu ^a  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Basic reproduction number; Minimal wave speed; Reaction diffusion equations; Repulsion of superinfecting virions; Spreading speed; Traveling wave solution

Indexed keywords

ANIMAL; BASIC REPRODUCTION NUMBER; BIOLOGICAL MODEL; CELLS; HOST PATHOGEN INTERACTION; HUMAN; MATHEMATICAL PHENOMENA; SUPERINFECTION; TIME FACTOR; TRANSMISSION; VIROLOGY; VIRUS INFECTION;

ANIMALS; BASIC REPRODUCTION NUMBER; CELLS; HOST-PATHOGEN INTERACTIONS; HUMANS; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; SUPERINFECTION; TIME FACTORS; VIRUS DISEASES;

EID: 84939877368     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-014-0033-9     Document Type: Article

References (32)

1. Adams RA (1975) Sobolev spaces. Academic Press, New York
2. Amann H (1989) Dynamical theory of quasilinear parabolic equations III: global existence. Math Z 202:219–250
3. Amann H (1993) Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In: Schmeisser HJ, Triebel H (eds) Function spaces, differential operators and nonlinear analysis (Friedrichroda, 1992), vol 133. Teubner-Texte zur Mathematik. Teubner, Stuttgart, pp 9–126
4. Beyn WJ (1990) The numerical computation of connecting orbits in dynamical systems. IMA J Numer Anal 9:379–405
5. Bonhoeffer S, May RM, Shaw GM, Nowak MA (1997) Virus dynamics and drug therapy. Proc Natl Acad Sci USA 94:6971
6. Chatelin F (1981) The spectral approximation of linear operators with application to the computation of eigenelements of differential and integral operators. SIAM Rev 23:495–522
7. Condit RC (2010) Surf and turf: mechanism of enhanced virus spread during poxvirus infection. Viruses 2:1050–1054
8. Doceul V, Hollinshead M, van der Linden L, Smith GL (2010) Repulsion of superinfecting virions: a mechanism for rapid virus spread. Science 327:873–876
9. Gan Q, Xu R, Yang P (2010) Travelling waves of a hepatitis B virus infection model with spatial diffusion and time delay. J Appl Math 75:392–417
10. Guo Z, Wang F-B, Zou X (2012) Threshold dynamics of an infective disease model with a fixed latent period and non-local infections. J Math Biol 65:1387–1410
11. Haberman R (1998) Elementary applied partial differential equations: with Fourier series and boundary value problems. Prentice Hall, New Jersey
12. Heffernan JM, Smith RJ, Wahl LM (2005) Perspectives on the basic reproductive ratio. J R Soc Interface 2(4):281–293
13. Ikebe Y (1972) The Galerkin method for the numerical solution of Fredholm integral equations of the 2nd kind. SIAM Rev 14:465–491
14. Komarova NL (2007) Viral reproductive strategies: how can lytic viruses be evolutionarily competitive? J Theor Biol 249:766–784
15. Korobeinikov A (2004) Global properties of basic virus dynamics models. Bull Math Biol 66:879–883
16. Li B, Weinberger HF, Lewis MA (2005) Spreading speeds as slowest wave speeds for cooperative systems. Math Biosci 196:82–98
17. Lewis MA, Li B, Weinberger HF (2002) Spreading speeds and linear determinacy for two-species competition models. J Math Biol 45:219–233
18. Lou Y, Zhao XQ (2011) A reaction–diffusion malaria model with incubation period in the vector population. J Math Biol 62:543–568
19. Mothes W, Sherer NM, Jin J, Zhong P (2010) Virus cell-to-cell transmission. J Virol 84:8360–8368
20. Murray JD (2000) Mathematical biology II: spatial models and biomedical applications. Springer, New York
21. Neubert MG, Parker IM (2004) Projecting rates of spread for invasive species. Risk Anal 24:817–831
22. Sattentau Q (2008) Avoiding the void: cell-to-cell spread of human viruses. Nat Rev Microbiol 6:815–826
23. Sattentau Q (2011) The direct passage of animal viruses between cells. Curr Opin Virol 1:396–402
24. Smith HL (1995) Monotone dynamic systems: an introduction to the theory of competitive and cooperative systems. Math Surveys Monogr, vol 41. American Mathematical Society, Providence, RI
25. Thieme HR (2009) Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity. SIAM J Appl Math 70:188–211
26. Vaidya NK, Wang F-B, Zou X (2012) Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment. Discrete Cont Dyn Syst B 17:2829–2848
27. Wang K, Wang W (2007) Propagation of HBV with spatial dependence. Math Biosci 210:78–95
28. Wang W, Zhao XQ (2011) A nonlocal and time-delayed reaction–diffusion model of dengue transmission. SIAM J Appl Math 71:147–168
29. Wang W, Zhao XQ (2012) Basic reproduction numbers for reaction diffusion epidemic models. SIAM J Appl Dyn Sys 11:1652–1673
30. Weinberger HF, Lewis MA, Li B (2002) Analysis of linear determinacy for spread in cooperative models. J Math Biol 45:183–218
31. Weinberger HF, Lewis MA, Li B (2007) Anomalous spreading speeds of cooperative recursion systems. J Math Biol 55:207–222
32. Xu R, Ma Z (2009) An HBV model with diffusion and time delay. J Theor Biol 257:499–509