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Dynamics of a general model of host-symbiont interaction

  • Received: 05 December 2018 Accepted: 11 March 2019 Published: 10 April 2019
  • We consider a model of host-symbiont interactions, in which symbionts can only live in association with their host and are transmitted both vertically from associated hosts to their offspring and horizontally from associated hosts to nearby unassociated hosts. The effect of the symbiont is modelled by a change in the birth rate of associated hosts. We analyze the two-dimensional dynamics in the resulting four-dimensional parameter space, and determine the qualitative behaviour for all parameter values. We find that for all but one choice of parameter values, solutions in the feasible region, apart from a 0- or 1-dimensional set of initial conditions, tend either to a unique equilibrium, or to one of two distinct equilibria. Moreover, the bistable case occurs only when the symbiont is a mutualist whose horizontal spread rate through the host population exceeds the positive change in the birth rate of associated hosts.

    Citation: Eric Foxall. Dynamics of a general model of host-symbiont interaction[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 3047-3070. doi: 10.3934/mbe.2019151

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  • We consider a model of host-symbiont interactions, in which symbionts can only live in association with their host and are transmitted both vertically from associated hosts to their offspring and horizontally from associated hosts to nearby unassociated hosts. The effect of the symbiont is modelled by a change in the birth rate of associated hosts. We analyze the two-dimensional dynamics in the resulting four-dimensional parameter space, and determine the qualitative behaviour for all parameter values. We find that for all but one choice of parameter values, solutions in the feasible region, apart from a 0- or 1-dimensional set of initial conditions, tend either to a unique equilibrium, or to one of two distinct equilibria. Moreover, the bistable case occurs only when the symbiont is a mutualist whose horizontal spread rate through the host population exceeds the positive change in the birth rate of associated hosts.


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    [1] N. Moran, The ubiquitous and varied role of infection in the lives of animals and plants, Amer. Nat. 160 (2002), S1–S8.
    [2] T. Fenchel, Ecology of Protozoa. Springer-Verlag, 1987.
    [3] C. C. Khor and M. L. Hibberd, Host-pathogen interactions revealed by human genome-wide surveys, Trends Genet. 28 (2012), 233–243.
    [4] D. Harvell, Ecology and evolution of host-pathogen interactions in nature, Amer. Nat. 164 (2004), S1–S5.
    [5] M. Li, B.Wang, M. Zhang, et al., Symbiotic gut microbes modulate human metabolic phenotypes, PNAS 105 (2008) 2117–2122.
    [6] R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, 1991.
    [7] C. L. Wolin and L. R. Lawlor, Models of facultative mutualism: density effects, Am. Nat., 124 (1984), 843–862.
    [8] D. H. Wright, A simple, stable model of mutualism incoporating handling time, Am. Nat., 134 (1989), 664–667.
    [9] M. Lipsitch, M. A. Nowak, D. Ebert, et al., The population dynamics of vertically and horizontally transmitted parasites, P. Roy. Soc. B-Biol. Sci., 260 (1995).
    [10] E. Foxall and N. Lanchier, Generalized stacked contact process with variable host fitness, arXiv:1511.01184 (2016).
    [11] S. J. Court, R. A. Blythe and R. J. Allen, Parasites on parasites: coupled fluctuations in stacked contact processes, EPL 101 (2013).
    [12] T. G. Kurtz, Strong approximation theorems for density dependent Markov chains, Stoch. Proc. Appl. 6 (1978), 223–240.
    [13] M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems Third Edition, Springer-Verlag, 2012.
    [14] G. O. Poinar, Description of an early Cretaceous termite (Isoptera: Kalotermitidae) and its associated intestinal protozoa, with comments on their co-evolution, Parasite. Vector., 2 (2009).
    [15] C. L.Wolin, The population dynamics of mutualistic systems. In: D. H. Boucher (ed.) The Biology of Mutualism, Oxford University Press, New York, (1985), 248–269.
    [16] H. Amann, Ordinary Differential Equations: an Introduction to Nonlinear Analysis. de Gruyter Studies in Mathematics, 13, 1990.
    [17] L. Perko, Differential Equations and Dynamical Systems. Third edition. Texts in Applied Mathematics, 7. Springer-Verlag, New York, 2001. xiv+553 pp.
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