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In this work we have investigated the evolutionary dynamics of a generalistpathogen, e.g. a virus population, that evolves towards specialisation in anenvironment with multiple host types. We have particularly explored under whichconditions generalist viral strains may rise in frequency and coexist withspecialist strains or even dominate the population. By means of a nonlinearmathematical model and bifurcation analysis, we have determined the theoreticalconditions for stability of nine identified equilibria and provided biologicalinterpretation in terms of the infection rates for the viral specialist andgeneralist strains. By means of a stability diagram we identified stable fixedpoints and stable periodic orbits, as well as regions of bistability. Forarbitrary biologically feasible initial population sizes, the probability ofevolving towards stable solutions is obtained for each point of the analyzedparameter space. This probability map shows combinations of infection rates ofthe generalist and specialist strains that might lead to equal chances for eachtype becoming the dominant strategy. Furthermore, we have identified infectionrates for which the model predicts the onset of chaotic dynamics. Severaldegenerate Bogdanov-Takens and zero-Hopf bifurcations are detected along withgeneralized Hopf and zero-Hopf bifurcations. This manuscript providesadditional insights into the dynamical complexity of host-pathogen evolutiontowards different infection strategies.

Host-virus evolutionary dynamics with specialist and generalist infection strategies: bifurcations, bistability and chaos