Multiple coexistence equilibria in a two parasitoid-one host model.

Briggs et al. (1993) introduced a host-parasitoid model for the dynamics of a system with two parasitoids that attack different juvenile stages of a common host. Their main result was that coexistence of the parasitoids is only possible when there is sufficient variability in the maturation delays of the host juvenile stages. Here, we analyze the phenomenon of coexistence in that model more deeply. We show that with some distribution families for the maturation delays, the coexistence equilibrium is unique, while with other distributions multiple coexistence equilibria can be found. In particular, we find that stable coexistence does not necessarily require mutual invasibility.

Considerations for Industry-Preparing for the FDA Model-Informed Drug Development (MIDD) Paired Meeting Program.

A recent industry perspective published in this journal describes the benefits received by drug companies from participation in the MIDD Pilot Program. Along with the primary objectives of supporting good decision-making in drug development, there were substantial savings in time and development costs. Furthermore, many sponsors reported qualitative benefits such as new learnings and clarity on MIDD strategies and methodology that could be applied to other development programs. Based on the success of the Pilot Program, the FDA recently announced the continuation of the MIDD Paired Meeting Program as part of the Prescription Drug User Fee Act (PDUFA VII). In this report, we describe the collective experiences of industry participants in the MIDD Program to date, including all aspects of the process from meeting request submission to follow-up actions. The purpose is to provide future participants with information to optimize the value of the MIDD Program.

An immuno-eco-epidemiological model of competition.

This paper introduces a novel immuno-eco-epidemiological model of competition in which one of the species is affected by a pathogen. The infected individuals from species one are structured by time-since-infection and the within-host dynamics of the pathogen and the immune response is also modelled. A novel feature of the model is the impact of the species two numbers on the ability of species one to mount an immune response. The within-host model has three equilibria: an extinction equilibrium, pathogen-only equilibrium and pathogen and immune response equilibrium which exists if the immune response reproduction number R0 > 1. The extinction equilibrium is always unstable, the pathogen-only equilibrium is stable if R0 < 1, and the coexistence equilibrium is stable whenever it exists. The between-host competition model has six equilibria: an extinction equilibrium, three disease-free equilibria: species one-only equilibrium, species two-only equilibrium and a disease-free species coexistence equilibrium. There are also two disease-present equilibria: species one-only disease equilibrium and disease coexistence equilibrium. The existence and stability of these equilibria are governed by six reproduction numbers. Results show that for a non-fatal disease, the disease coexistence equilibrium is stable whenever it exists.

Oscillations in a size-structured prey-predator model.

This article introduces a predator-prey model with the prey structured by body size, based on reports in the literature that predation rates are prey-size specific. The model is built on the foundation of the one-species physiologically structured models studied earlier. Three types of equilibria are found: extinction, multiple prey-only equilibria and possibly multiple predator-prey coexistence equilibria. The stabilities of the equilibria are investigated. Comparison is made with the underlying ODE Lotka-Volterra model. It turns out that the ODE model can exhibit sustain oscillations if there is an Allee effect in the net reproduction rate, that is the net reproduction rate grows for some range of the prey's population size. In contrast, it is shown that the structured PDE model can exhibit sustain oscillations even if the net reproductive rate is strictly declining with prey population size. We find that predation, even size-non-specific linear predation can destabilize a stable prey-only equilibrium, if reproduction is size specific and limited to individuals of large enough size. Furthermore, we show that size-specific predation can also destabilize the predator-prey equilibrium in the PDE model. We surmise that size-specific predation allows for temporary prey escape which is responsible for destabilization in the predator-prey dynamics.