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.
Highlights
It is well known that the relationship between hosts and parasites is extremely convoluted [9, 17]
Superinfection and a trade-off involving production rate by infected hosts and their recovery rate are considered in a basic SIR model with two parasite strains and one host strain
We obtain a positive equilibrium representing the coexistence of parasite strains 1 and 2 in the resident host and prove its local stability
Summary
It is well known that the relationship between hosts and parasites is extremely convoluted [9, 17]. Parasites harm hosts and possibly cause deaths to the hosts, they live on or in the bodies of the hosts and are dependent on them. Host-parasite co-evolution is still a ubiquitous phenomenon of potential importance to all living organisms, including humans. Many medically relevant diseases (e.g. malaria, AIDS and influenza) are caused by co-evolving parasites. Better understanding of the co-evolutionary adaptation between parasite “attack strategy” and host “defence strategy” (i.e. immunological response), may result in discovery/development of novel medications and vaccines and help save human lives [31]
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