Models of cytokine dynamics in the inflammatory response of viral zoonotic infectious diseases

Abstract

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.

Quantification of Cytokine Storms During Virus Infections

“…A large number of studies have developed cytokine changes into boolean models, and then, converted the models to ordinary differential equations (ODEs) that helped to reveal the behaviour of the various cytokines (31)(32)(33)(34)(35)(36). However, these reports mainly focused on dynamics of individual cytokines (31,32,(34)(35)(36) or cytokine groups (such as pro-inflammatory cytokine group and anti-inflammatory cytokine group) (33). Interactions among IL-4, IFN-g and cytokines with the largest induction amplitudes have not been modeled before.…”

Stability Analysis of a Mathematical Model in Inflammatory Response System Due to SARS Coronavirus Infection

“…SARS Coronavirus berkembang biak pada inang alaminya, yaitu kelelawar [8], [10]. Manusia bukan merupakan inang alami dan hanya terinfeksi melalui interaksi dengan inang alaminya, baik secara langsung maupun tidak langsung melalui lingkungan, seperti menghirup kotoran inang alami atau pembawanya [22].…”

“…Model matematika sistem respon inflamasi akibat adanya infeksi virus telah dikonstruksi pada [22]. Namun, model matematika tersebut memiliki struktur yang kompleks, sehingga analisis kestabilan titik ekuilibrium model belum dilakukan.…”

“…Sistem respon inflamasi manusia terhadap infeksi SARS Coronavirus terdiri atas interaksi antara sitokin pro-respon dengan anti-respon inflamasi [22]. Inflamasi akibat adanya infeksi SARS Coronavirus direspon oleh sitokin pro-respon inflamasi untuk mengurangi dampak inflamasi.…”

Mathematical model of a cytokine storm

“…Hopkins et al (12) created a model of 9 major cytokines affecting the outcome of CAR-T cell based therapy. A smaller more conceptual model was proposed by Baker et al (13), where a two-dimensional system of equations captured interactions between pro- and anti-inflammatory cytokines, displaying large regions of bi-stability and oscillations reminiscent of immune behavior in rheumatoid arthritics; the model was later extended by other authors, such as by Zhang et al (14).…”