An immuno-eco- epidemiological model of competition

The ecological interactions between species can influence host-pathogen dynamics.  For example, shared pathogens can lead to indirect completion between species, and pathogens of a single species can shift competitive outcomes of that species with other non-susceptible, or non-target species.  In this paper, the authors create a model describing how competition between two species affects the immune response of one of the two species, which hosts a pathogen that cannot infect the other, coupled to a model for how the pathogen’s dynamics within the host and its immune response feeds back to influence the population-level competitive outcome between the host and its competitor. Specifically, hey use a partial differential equation (PDE) model that links Lotka-Volterra competition into an SI epidemic model, to describe population dynamics of the two species.  Then, they use an ordinary differential equation (ODE) model to describe the pathogen population growth within a host and the immune system clearing rate of the pathogen, the latter of which is modified (in a negative direction) by the abundance of the competitor species.  They define the rate of removal of the infected hosts from the population to within-host viral load at a specific age-since-infection, multiplied by a proportionality constant.  They similarly link the rate of infection in the population to within-host viral load.  Thus, they nest within-host pathogen-immune system dynamics in between-host transmission.

By studying the local and global stability of the within-host (ODE) model, they find that both the virus and the immune system can persist if the immune response reproduction number is > 1 (and thus the infection is chronic).  This reproduction number is negatively affected by the equilibrial abundance of the non-host competitor, so that the host’s immune response is weakened with the increasing abundance of its competitor.  In the PDE model, there were six equilibria, including three disease-free equilibria, one of which had coexistence between the two competitors, given the right range of reproduction numbers.  However, if the disease is non-fatal, the two species could coexist stably with the disease present, across a specific range of basic reproduction rates for the two species.  Overall, this set of models indicated that the outcome of competition between the two species was affected by the within-host dynamics of the pathogen, and provided a useful example of how ecological interactions can be explicitly linked in a theoretical framework to host-pathogen dynamics.

Souvik Bhattacharya & Maia Martcheva (2016) An immuno-eco- epidemiological model of competition, Journal of Biological Dynamics, 10:1, 314-341, DOI: 10.1080/17513758.2016.1186291