Epidemics with mutating infectivity on small-world networks

Год публикации
Rüdiger S; Plietzsch A; Sagués F; Sokolov I; Kurths Jü

Epidemics and evolution of many pathogens occur on similar timescales so that their dynamics are often entangled. Here, in a first step to study this problem theoretically, we analyze mutating pathogens spreading on simple SIR networks with grid-like connectivity. We have in mind the spatial aspect of epidemics, which often advance on transport links between hosts or groups of hosts such as cities or countries. We focus on the case of mutations that enhance an agent’s infection rate. We uncover that the small-world property, i.e., the presence of long-range connections, makes the network very vulnerable, supporting frequent supercritical mutations and bringing the network from disease extinction to full blown epidemic. For very large numbers of long-range links, however, the effect reverses and we find a reduced chance for large outbreaks. We study two cases, one with discrete number of mutational steps and one with a continuous genetic variable, and we analyze various scaling regimes. For the continuous case we derive a Fokker-Planck-like equation for the probability density and solve it for small numbers of shortcuts using the WKB approximation. Our analysis supports the claims that a potentiating mutation in the transmissibility might occur during an epidemic wave and not necessarily before its initiation.

Библиографический список
  1. Dawood, F. S. et al. Estimated global mortality associated with the first 12 months of 2009 pandemic influenza A H1N1 virus circulation: a modelling study. The Lancet infectious diseases 12, 687 (2012).
  2. WHO: Ebola situation report 30 March 2016 (2016).
  3. Danon, L. et al. Networks and the epidemiology of infectious disease. 2011 (2011).
  4. Moore, C. & Newman, M. E. Epidemics and percolation in small-world networks. Physical Review E. 61 5, 5678 (2000).
  5. Sander, L., Warren, C., Sokolov, I., Simon, C. & Koopman, J. Percolation on heterogeneous networks as a model for epidemics. Mathematical Biosciences 180, 293 (2002).
  6. Colizza, V., Pastor-Satorras, R. & Vespignani, A. Reaction-diffusion processes and metapopulation models in heterogeneous networks. Nature Physics 3, 276 (2007).
  7. Pastor-Satorras, R., Castellano, C., Van Mieghem, P. & Vespignani, A. Epidemic processes in complex networks. Reviews of Modern Physics 87, 925 (2015).
  8. R. Cohen & S. Havlin, Complex networks: structure, robustness and function (Cambridge university press, 2010).
  9. Wang, W., Tang, M., Stanley, H. E. & Braunstein, L. A. Unification of theoretical approaches for epidemic spreading on complex networks. Reports on Progress in Physics 80, 036603 (2017).
  10. M. Newman, Networks: an introduction (Oxford university press, 2010).
  11. Barthélemy, M. Spatial networks. Physics Reports 499, 1 (2011).
  12. Sun, G.-Q., Jusup, M., Jin, Z., Wang, Y. & Wang, Z. Pattern transitions in spatial epidemics: Mechanisms and emergent properties. Physics of Life Reviews 19, 43 (2016).
  13. Amaral, L. A. N., Scala, A., Barthelemy, M. & Stanley, H. E. Classes of small-world networks. Proceedings of the National Academy of Sciences 97, 11149 (2000).
  14. Sule, W. F. et al. Epidemiology and ecology of West Nile virus in sub-Saharan Africa. Parasites & Vectors 11, 414 (2018).
  15. Duffy, S. Why are RNA virus mutation rates so damn high? PLoS Biology 16, e3000003 (2018).
  16. Pybus, O. G. & Rambaut, A. Evolutionary analysis of the dynamics of viral infectious disease. Nature Reviews Genetics 10, 540 (2009).
  17. Pybus, O. G., Tatem, A. J. & Lemey, P. Virus evolution and transmission in an ever more connected world. Proceedings of the Royal Society B: Biological Sciences 282, 20142878 (2015).
  18. Diehl, W. E. et al. Ebola virus glycoprotein with increased infectivity dominated the 2013–2016 epidemic. Cell 167, 1088 (2016).
  19. Urbanowicz, R. A. et al. Human adaptation of Ebola virus during the West African outbreak. Cell 167, 1079 (2016).
  20. Iwasa, Y., Michor, F. & Nowak, M. A. Stochastic tunnels in evolutionary dynamics. Genetics 166, 1571 (2004).
  21. Weinreich, D. M. & Chao, L. Rapid evolutionary escape by large populations from local fitness peaks is likely in nature. Evolution 59, 1175 (2005).
  22. Altland, A., Fischer, A., Krug, J. & Szendro, I. G. Rare events in population genetics: stochastic tunneling in a two-locus model with recombination. Physical Review Letters 106, 088101 (2011).
  23. Russell, C. A. et al. The potential for respiratory droplet-transmissible A/H5N1 influenza virus to evolve in a mammalian host. Science 336, 1541 (2012).
  24. Longdon, B., Brockhurst, M. A., Russell, C. A., Welch, J. J. & Jiggins, F. M. The evolution and genetics of virus host shifts. PLoS Pathogens 10, e1004395 (2014).
  25. Bonneaud, C., Weinert, L. A. & Kuijper, B. Understanding the emergence of bacterial pathogens in novel hosts. Philosophical Transactions of the Royal Society B 374, 20180328 (2019).
  26. Cooper, J. D., Neuhauser, C., Dean, A. M. & Kerr, B. Tipping the mutation-selection balance: Limited migration increases the frequency of deleterious mutants. Journal of Theoretical Biology 380, 123 (2015).
  27. A. Bunde & Havlin S. Percolation I in Fractals and Disordered Systems (Springer, 1996), pp. 59–114.
  28. Newman, M. E. Spread of epidemic disease on networks. Physical Review E 66, 016128 (2002).
  29. Watts, D. J. & Strogatz, S. H. Collective dynamics of small-world networks. Nature 393, 440 (1998).
  30. Holmes, E. C., Dudas, G., Rambaut, A. & Andersen, K. G. The evolution of Ebola virus: Insights from the 2013–2016 epidemic. Nature 538, 193 (2016).
  31. M. A. Nowak, Evolutionary dynamics (Harvard University Press, 2006).
  32. De Visser, J. A. G. & Krug, J. Empirical fitness landscapes and the predictability of evolution. Nature Reviews Genetics 15, 480 (2014).
  33. D. Stauffer & A. Aharony, Introduction to percolation theory (Taylor & Francis, 2014).
  34. Bedford, T. & Malik, H. S. Did a single amino acid change make Ebola virus more virulent? Cell 167, 892 (2016).
  35. Judson, S., Prescott, J. & Munster, V. Understanding ebola virus transmission. Viruses 7, 511 (2015).
  36. May, R. M. & Lloyd, A. L. Infection dynamics on scale-free networks. Physical Review E 64, 066112 (2001).
  37. Wang, Y., Ma, J., Cao, J. & Li, L. Edge-based epidemic spreading in degree-correlated complex networks. Journal of Theoretical Biology 454, 164 (2018).
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