Conceiving innate immunity as a predator-prey system with a refuge: Modeling and simulation

Background/Question/Methods

Innate immunity is a defense against pathogens found in many animals, including humans. When pathogenic bacteria invade the body, this defense system elicits phagocytic cells to destroy the pathogen by predation. In response, pathogenic bacteria can seek refuge by entering an intracellular or communal environment, such as a biofilm. This is analogous to a predator-prey model, in which the body’s phagocytic cells are the predator seeking out the prey, the pathogens. Although this process is one of the most important defense mechanisms against infection, little is known about its kinetics. A mathematical model has been constructed in terms of phagocytes and two types of pathogenic bacteria: free bacteria susceptible to phagocytes and bacteria with an intracellular or biofilm refuge that cannot be phagocytized. The equilibria and stability of the resulting system of differential equations was analzyed, and dynamics were visualized by numerical simulations.

Results/Conclusions

Equilibria and their stabilitly depended on the parameters of the model. Infections could not persist unless the growth rate of the bacteria was sufficiently high. The recruitment of phagocytes to an infection site was either contant or increased in response to a signal dependent on pathogen density. The analysis showed that a constant input of phagocytes to the infection site is required for an infection to clear.