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Seminar on mathematical modeling in biology and medicine
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A mathematical model of coevolutionary dynamics of a replicator and a virus A. S. Bratus'ab, S. V. Drozhzhinb, A. S. Novozhilovc a Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow b Russian University of Transport c North Dakota State University |
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Abstract: A novel mathematical framework is proposed to describe the ecological and evolutionary consequences of replicator–virus interactions. Both the replicator and virus are assumed to consist of several (sub)species, which interact between themselves, forming a complex and evolving replicator network, in addition to the host–parasite type interaction between themselves. Separating the ecological and evolutionary time scales, we allow our mathematical model to evolve, with the evolutionary steps chosen according to the replicator’s and virus’ objective functions, through which they both aim to maximize their evolutionary success at the opponent’s expense. While the resulting model is complex, and intractable analytically, we propose a simple and efficient heuristic numerical algorithm that leads to systems’ coevolution. Numerical simulations show that the model, along with the expected outcomes of either replicator or virus winning the evolutionary battle, is capable of producing also a (quasi)stationary state of replicator–virus coexistence with monotone growth of both the replicator and virus fitnesses. In this (quasi)stationary state, quite primitive originally the network of inter-population interactions of replicator evolves into a complex and robust network capable to withstand the adverse effects of the virus. Such stable states highlight the importance of the intra-population evolution, which, despite the opposite evolutionary goals of the replicator and the virus, leads to long term ecological coexistence and highlights the paradigm that viruses should be considered outside of simplistic interpretation as parasites; on the contrary, they are necessary for the replicator to increase its complexity to be prepared for future evolutionary challenges. Language: English |
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