A Mathematical Framework for Predicting Lifestyles of Viral Pathogens
Tóm tắt
Despite being similar in structure, functioning, and size, viral pathogens enjoy very different, usually well-defined ways of life. They occupy their hosts for a few days (influenza), for a few weeks (measles), or even lifelong (HCV), which manifests in acute or chronic infections. The various transmission routes (airborne, via direct physical contact, etc.), degrees of infectiousness (referring to the viral load required for transmission), antigenic variation/immune escape and virulence define further aspects of pathogenic lifestyles. To survive, pathogens must infect new hosts; the success determines their fitness. Infection happens with a certain likelihood during contact of hosts, where contact can also be mediated by vectors. Besides structural aspects of the host-contact network, three parameters appear to be key: the contact rate and the infectiousness during contact, which encode the mode of transmission, and third the immunity of susceptible hosts. On these grounds, what can be said about the reproductive success of viral pathogens? This is the biological question addressed in this paper. The answer extends earlier results of the author and makes explicit connection to another basic work on the evolution of pathogens. A mathematical framework is presented that models intra- and inter-host dynamics in a minimalistic but unified fashion covering a broad spectrum of viral pathogens, including those that cause flu-like infections, childhood diseases, and sexually transmitted infections. These pathogens turn out as local maxima of numerically simulated fitness landscapes. The models involve differential and integral equations, agent-based simulation, networks, and probability.
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Tài liệu tham khảo
Alizon S, Hurford A, Mideo N, van Baalen M (2009) Virulence evolution and the trade-off hypothesis: history, current state of affairs and the future. J Evol Biol 22:245–259
Alizon S, Luciani F, Regoes RR (2011) Epidemiological and clinical consequences of within-host evolution. Trends Microbiol 19:24–32
Alizon S, de Roode JC, Michalakis Y (2013) Multiple infections and the evolution of virulence. Ecol Lett 16:556–567
Clay PA, Rudolf VHW (2019) How parasite interaction strategies alter virulence evolution in multi-parasite communities. Evolution 73:2189–2203
Coombs D, Gilchrist MA, Ball CL (2007) Evaluating the importance of within- and between-host selection pressures on the evolution of chronic pathogens. Theor Popul Biol 72:576–591
Cortez MH (2013) When does pathogen evolution maximize the basic reproductive number in well-mixed host–pathogen systems? J Math Biol 67:1533–1585
Debye P, Hückel E (1923) The theory of electrolytes. I. Lowering of freezing point and related phenomena. Phys Z 24:185–206
Delamater PL, Street EJ, Leslie TF, Yang YT, Jacobsen KH (2019) Complexity of the basic reproduction number (R0). Emerg Infect Dis 25:1–4
Dieckmann U (2002) Adaptive dynamics of pathogen–host interactions. In: Dieckmann U, Metz JAJ, Sabelis MW, Sigmund K (eds) Adaptive dynamics of infectious diseases: pursuit of virulence management. Cambridge University Press, Cambridge, pp 39–59
Diekmann O, Heesterbeek JAP, Metz JAJ (1990) On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J Math Biol 28:365–382
Ferguson NM, Donnelly CA, Anderson RM (1999) Transmission dynamics and epidemiology of dengue: insights from age-stratified sero-prevalence surveys. Philos Trans R Soc Lond B Biol Sci 354:757–768
Fraser C, Hollingsworth TD, Chapman R, de Wolf F, Hanage WP (2007) Variation in HIV-1 set-point viral load: epidemiological analysis and an evolutionary hypothesis. Proc Natl Acad Sci USA 104:17441–17446
Fraser C, Lythgoe K, Leventhal GE, Shirreff G, Hollingsworth TD, Alizon S, Bonhoeffer S (2014) Virulence and pathogenesis of HIV-1 infection: an evolutionary perspective. Science 343:1243727
Fuller TL, Gilbert M, Martin V, Cappelle J, Hosseini P, Njabo KY, Aziz AS, Xiao X, Daszak P, Smith TB (2013) Predicting hotspots for influenza virus reassortment. Emerg Infect Dis 19:581–588
Georgieva M, Buckee CO, Lipsitch M (2019) Models of immune selection for multi-locus antigenic diversity of pathogens. Nat Rev Immunol 19:55–62
Geritz SAH, Kisdi E, Meszena G, Metz JAJ (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol Ecol 12:35–57
Gog JR, Pellis L, Wood JLN, McLean AR, Arinaminpathy N, Lloyd-Smith JO (2015) Seven challenges in modelling pathogen dynamics within-host and across scales. Epidemics 10:45–48
Grenfell BT, Pybus OG, Gog JR, Wood JLN, Daly JM, Mumford JA, Holmes EC (2004) Unifying the epidemiological and evolutionary dynamics of pathogens. Science 303:327–332
Guerra FM, Bolotin S, Lim G, Heffernan J, Deeks SL, Li Y, Crowcroft NS (2017) The basic reproduction number (R0) of measles: a systematic review. Lancet Infect Dis 17:e420–e428
Gulbudak H, Weitz JS (2019) Heterogeneous viral strategies promote coexistence in virus-microbe systems. J Theor Biol 462:65–84
Gyllenberg M, Service R (2011) Necessary and sufficient conditions for the existence of an optimisation principle in evolution. J Math Biol 62:359–369
Handel A, Rohani P (2015) Crossing the scale from within-host infection dynamics to between-host transmission fitness: a discussion of current assumptions and knowledge. Philos Trans R Soc B 370:20140302
Handel A, Brown J, Stallknecht D, Rohani P (2013) A multi-scale analysis of influenza A virus fitness trade-offs due to temperature-dependent virus persistence. PLoS Comput Biol 9:e1002989
Handel A, Lebarbenchon C, Stallknecht D, Rohani P (2014) Trade-offs between and within scales: environmental persistence and within-host fitness of avian influenza viruses. Proc R Soc B 281:20133051
Hartlage AS, Cullen JM, Kapoor A (2016) The strange, expanding world of animal hepaciviruses. Annu Rev Virol 3:53–75
Herfst S, Schrauwen EJA, Linster M, Chutinimitkul S, de Wit E, Munster VJ, Sorrell EM, Bestebroer TM, Burke DF, Smith DJ, Rimmelzwaan GF, Osterhaus ADME, Fouchier RAM (2012) Airborne transmission of influenza A/H5N1 virus between ferrets. Science 336:1534–1541
Johnson PLF, Kochin BF, Ahmed R, Antia R (2012) How do antigenically varying pathogens avoid cross-reactive responses to invariant antigens? Proc R Soc B 279:2777–2785
Klenerman P, Hill A (2005) T cells and viral persistence: lessons from diverse infections. Nat Immunol 6:873–879
Lange A (2016) Reconstruction of disease transmission rates: applications to measles, dengue, and influenza. J Theor Biol 400:138–153
Lange A, Ferguson NM (2009) Antigenic diversity, transmission mechanisms, and the evolution of pathogens. PLoS Comput Biol 5(10):e1000536
Levin BR (1996) The evolution and maintenance of virulence in microparasites. Emerg Infect Dis 2:93–102
Lewis F, Hughes GJ, Rambaut A, Pozniak A, Leigh Brown AJ (2008) Episodic sexual transmission of HIV revealed by molecular phylodynamics. PLoS Med 5(3):e50
Li Y, Handel A (2014) Modeling inoculum dose dependent patterns of acute virus infections. J Theor Biol 347:63–73
Li J, Blakeley D, Smith RJ (2011) The failure of R0. Comput Math Methods Med 2011: 527610. https://doi.org/10.1155/2011/527610
Lloyd-Smith JO, Funk S, McLean AR, Riley S, Wood JL (2015) Nine challenges in modelling the emergence of novel pathogens. Epidemics 10:35–39
Luciani F, Alizon S (2009) The evolutionary dynamics of a rapidly mutating virus within and between hosts: the case of hepatitis C virus. PLoS Comput Biol 5:e1000565
Messinger SM, Ostling A (2013) Predator attack rate evolution in space: the role of ecology mediated by complex emergent spatial structure and self-shading. Theor Pop Biol 89:55–63
Metz JAJ, Mylius SD, Diekmann O (2008) When does evolution optimize? Evol Ecol Res 10:629–654
Murillo LN, Murillo MS, Perelson AS (2013) Towards multiscale modeling of influenza infection. J Theor Biol 332:267–290
Mylius SD, Diekmann O (1995) On evolutionarily stable life histories, optimization and the need to be specific about density dependence. Oikos 74:218–224
Pepin KM, Volkov I, Banavar JR, Wilke CO, Grenfell BT (2010) Phenotypic differences in viral immune escape explained by linking within-host dynamics to host-population immunity. J Theor Biol 265:501–510
Read JM, Keeling MJ (2003) Disease evolution on networks: the role of contact structure. Proc R Soc Lond B 270:699–708
Rehermann B (2009) Hepatitis C virus versus innate and adaptive immune responses: a tale of coevolution and coexistence. J Clin Invest 119:1745–1754
Ssematimba A, Hagenaars TJ, de Jong MCM (2012) Modelling the wind-borne spread of highly pathogenic avian influenza virus between farms. PLoS ONE 7(2):e31114
Weitz JS, Li G, Gulbudak H, Cortez MH, Whitaker RJ (2019) Viral invasion fitness across a continuum from lysis to latency. Virus Evol 5:vez006
Wherry EJ, Kurachi M (2015) Molecular and cellular insights into T cell exhaustion. Nat Rev Immunol 15:486–499