An immuno-eco-epidemiological model of competition

Mathematical methods for scaling from within-host to population-scale in infectious disease systems

Mathematical modellers model infectious disease dynamics at different scales. Within-host models represent the spread of pathogens inside an individual, whilst between-host models track transmission between individuals. However, pathogen dynamics at one scale affect those at another. This has led to the development of multiscale models that connect within-host and between-host dynamics. In this article, we systematically review the literature on multiscale infectious disease modelling according to PRISMA guidelines, dividing previously published models into five categories governing their methodological approaches (Garira (2017)), explaining their benefits and limitations. We provide a primer on developing multiscale models of infectious diseases.

Stationary status of discrete and continuous age-structured population models

From Leonhard Euler to Alfred Lotka and in recent years understanding the stationary process of the human population has been of central interest to scientists. Population reproductive measure NRR (net reproductive rate) has been widely associated with measuring the status of population stationarity and it is also included as one of the measures in the millennium development goals. This article argues how the partition theorem-based approach provides more up-to-date and timely measures to find the status of the population stationarity of a country better than the NRR-based approach. We question the timeliness of the value of NRR in deciding the stationary process of the country. We prove associated theorems on discrete and continuous age distributions and derive measurable functional properties. The partitioning metric captures the underlying age structure dynamic of populations at or near stationarity. As the population growth rates for an ever-increasing number of countries trend towards replacement levels and below, new demographic concepts and metrics are needed to better characterize this emerging global demography.

Host traits and competitive ability jointly structure disease dynamics and community assembly

Parasitism and competition are both ubiquitous interactions in ecological communities. The ability of host species to interact directly via competition and indirectly through shared parasites suggests that host traits related to competition and parasitism are likely important in structuring communities and disease dynamics. Specifically, those host traits affecting competition and those mediating parasitism are often correlated either because of trade-offs (in resource acquisition or resource allocation) or condition dependence, yet the consequences of these trait relationships for community and epidemiological dynamics are poorly understood. We conducted a literature review of parasite-related host traits-competitive ability relationships. We found that transmission-competitive ability relationships were most often reported, and that superior competitors exhibited elevated transmission relative to their less-competitive counterparts in nearly 80% of the cases. We also found a significant number of virulence-competitive ability and parasite shedding-competitive ability relationships. We investigated these links by altering the relationship between host competitive ability and three parasite-related traits (transmission, virulence and parasite shedding rates) in a simple model, incorporating competitive asymmetries in a multi-host community. We show that these relationships can lead to a range of different communities. For example, depending on the strength and direction of these distinct trait relationships, we observed communities with anywhere from high parasite prevalence to complete parasite extinction, and either one, two or the maximum of three host species coexisting. Our results suggest that parasite-competitive ability relationships may be common in nature, that further integration of these relationships can produce novel and unexpected community and disease dynamics, and that generalizations may allow for the prediction of how parasitism and competition jointly structure disease and diversity in natural communities.

Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model

This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed stress-induced competition. When the disease is chronic, and the within-host dynamics are rapid, we reduce the partial differential equation model (PDE) to a three-dimensional ordinary differential equation (ODE) model. The ODE model exhibits backward bifurcation and sustained oscillations caused by the stress-induced competition. Furthermore, the ODE model, although not a special case of the PDE model, is useful for detecting backward bifurcation and oscillations in the PDE model. Backward bifurcation related to stress-induced competition allows the second species to persist for values of its invasion number below one. Furthermore, stress-induced competition leads to destabilization of the coexistence equilibrium and sustained oscillations in the PDE model. We suggest that complex systems such as this one may be studied by appropriately designed simple ODE models.