Immune-Pathogen Dynamics

Motivated by curiosities of disease progression seen in the coronavirus pandemic, we analyze a minimalist predator-prey model for the immune system (predator), competing against a pathogen (prey). We find that the mathematical model alone accounts for numerous paradoxical behaviors observed in this and other infections. These include why an exponentially growing pathogen requires an exposure threshold to take hold, how chronic and recurrent infections can arise, and what can allow very sick patients to recover, while healthier patients succumb. We also examine the distinct dynamical roles that nonspecific, "innate,"and specific, "adaptive,"immunity play, and we describe mathematical effects of infection history on prognosis. Finally, we briefly discuss predictions for some of the effects of timing and strengths of antibiotics or immunomodulatory agents.