Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Effects of superinfection and cost of immunity on host-parasite co-evolution

Pages: 809 - 829, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017040

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Liman Dai - Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A 3K7, Canada (email)
Xingfu Zou - Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A 3k7, Canada (email)

Abstract: In this paper, we investigate the cost of immunological up- regulation caused by infection in a between-host transmission dynamical model with superinfection. After introducing a mutant host to an existing model, we explore this problem in (A) monomorphic case and (B) dimorphic case. For (A), we assume that only strain 1 parasite can infect the mutant host. We identify an appropriate fitness for the invasion of the mutant host by analyzing the local stability of the mutant free equilibrium. After specifying a trade-off between the production and recovery rates of infected hosts, we employ the adaptive dynamical approach to analyze the evolutionary and convergence stabilities of the corresponding singular strategy, leading to some conditions for continuously stable strategy, evolutionary branching point and repeller. For (B), a new fitness is introduced to measure the invasion of mutant host under the assumption that both parasite strains can infect the mutant host. By considering two trade-off functions, we can study the conditions for evolutionary stability, isoclinic stability and absolute convergence stability of the singular strategy. Our results show that the host evolution would not favour high degree of immunological up-regulation; moreover, superinfection would help the parasite with weaker virulence persist in hosts.

Keywords:  Dimorphic adaptive dynamics, mutant, co-evolution, superinfection, up-regulation, trade-off function.
Mathematics Subject Classification:  Primary: 92D30, 92D25; Secondary: 34C25, 34C60.

Received: November 2015;      Revised: May 2016;      Available Online: January 2017.