Models of Cytokine Dynamics in the Inflammatory Response of Viral Zoonotic Infectious Diseases

Inflammatory responses to an infection from a zoonotic pathogen, such as avian influenza viruses, hantaviruses and some coronaviruses, are distinctly different in their natural reservoir versus human host. While not as well studied in the natural reservoirs, the pro-inflammatory response and viral replication appear controlled and show no obvious pathology. In contrast, infection in humans results in an initial high viral load marked by an aggressive pro-inflammatory response known as a cytokine storm. The key difference in the course of the infection between the reservoir and human host is the inflammatory response. In this investigation, we apply a simple two-component differential equation model for pro-inflammatory and anti-inflammatory responses and a detailed mathematical analysis to identify specific regions in parameter space for single stable endemic equilibrium, bistability or periodic solutions. The extensions of the deterministic model to two stochastic models account for variability in responses seen at the cell (local) or tissue (global) levels. Numerical solutions of the stochastic models exhibit outcomes that are typical of a chronic infection in the natural reservoir or a cytokine storm in human infection. In the chronic infection, occasional flare-ups between high and low responses occur when model parameters are in a region of bistability or periodic solutions. The cytokine storm with a vigorous pro-inflammatory response and less vigorous anti-inflammatory response occurs in the parameter region for a single stable endemic equilibrium with a strong pro-inflammatory response. The results of the model analyses and the simulations are interpreted in terms of the functional role of the cytokines and the inflammatory responses seen in infection of the natural reservoir or of the human host.