Abstract:
In an ecological system pathogens often need to share their host with other pathogens, and therefore compete for the resources with different spreading strategies. They can interact in different manners: for a short period cooperation between pathogens can lead to faster and larger host occupation [1-7]. Spanish Flu and HIV are examples of such cases. The cooperation, however, can lead to death of the host population and consequently also pathogens’ death. Therefore on a long run, the cooperation strategy is not necessary the best. We propose and study an evolutionary game model in order to understand the co-evolutionary dynamics of two co-infecting pathogens [8]. They have a common host and the host does not evolve on the same time scale as the pathogens. We consider two kind of disease species, while each of them have two different strategies: cooperation and defection. Agents (pathogens) accumulate a payoff, based on the history of their contagion records. This gives rise to two main scenarios: The first is when the disease infects an empty host. In this scenario, the pathogen does not meet any resistance, and all the host resources are available to him. But when the host is already occupied by another disease, things become a bit more complicated. More specifically in the second scenario, there are four possible combinations of pairs of strategies: (C, C), (C, D), (D, C) and (D, D) corresponding to different payoffs; A cooperator pathogen does not show any resistance to the contagion by another disease and will share the host resources with it. However, a defector entering a host populated by a cooperator will seize the majority of available resources. Considering Hawk-Dove game, in a mean-field approximation, we first show under which conditions cooperation may or may not be a meaningful strategy. Then we show how evolution affects spreading dynamics, and if and how any strategy can win. Finally we show how underlying transmission and contact networks may promote both the spreading and the emergence of cooperation.
Moreover, we show non-trivial dynamical effects of cooperation and competition in an ecological framework [9, 10]; we study two strains competing with each other for host resources in the presence of a third pathogen cooperating with both of them. We treat dynamics in a homogeneously mixed population by means of mean-field theory and stability analysis and also on complex transmission networks. We study the impact of cooperation on the outcome of the two-pathogen competition, which can be quantified in terms of dominance of one competing pathogen or the co- circulation of both of them. We show that the presence of a third cooperating pathogen can alter the outcome of competition as it may favor the more cooperative pathogen over the more infectious one.
[1] L. Chen, F Ghanbarnejad, W. Cai, P. Grassberger, EPL 104, 5 (2013).
[2] W. Cai, L. Chen, F. Ghanbarnejad, P. Grassberger, Nature Physics 11, 936 (2015).
[3] P. Grassberger, L. Chen, F. Ghanbarnejad, W. Cai, Physical Review E 93, 042316 (2016).
[4] J. P. Rodríguez, F. Ghanbarnejad, V. M. Eguíluz, Frontiers in Physics, V 5, P 46 (2017).
[5] S. Sajjadi, F. Karimi, M. R. Ejtehadi, F. Zarei, S. Moghimi-Araghi, F. Ghanbarnejad, “Coinfection in different time scales”, manuscript in preparation. [6] L. Chen, F. Ghanbarnejad, D. Brockmann, New J. Phys. 19, 103041(2017).
[7] J. P. Rodríguez, F. Ghanbarnejad, V. M. Eguíluz, “How mobility affect cooperative spreading diseases”, manuscript in preparation.
[8] F. Ghanbarnejad, K. Seegers, A. Cardillo, P. Hoevel, “Evolutionary cooperation, yes or no?”, manuscript in preparation.
[9] F. Pinotti, F. Ghanbarnejad, P. Hoevel, C. Poletto, “How to compete in presence of a cooperative agent”, manuscript in preparation.
[10] S. Meloni, F. Ghanbarnejad, Y. Moreno “coinfection on multilayer networks”, manuscript in preparation.