Today is
  • Mathematics study
Position: English > NEWS > NEWS > Content

Deterministic and Stochastic Models and Analyses for the Inflammatory Response in Viral Zoonotic Infectious Diseases


Academic Report

Title: Deterministic and Stochastic Models and Analyses for the Inflammatory Response in Viral Zoonotic Infectious Diseases

Reporter: Wenjing Zhang  Texas Tech University

Time: December 19, 2017 (Tuesday) PM 4:00-5:00

Location: A#1101 room, Innovation Park Building

Contact: Prof. LU Yufeng (tel: 84708351-8127)


Abstract: Inflammatory responses against pathogen infections in zoonotic diseases, such as avian influenza, hantavirus, and SARS-CoV, have distinct differences in humans and their natural reservoirs. In natural reservoirs the infection is persistent and often lasts the life of the animal. However, the spillover infection to humans causes a cytokine storm with severe disease and potential mortality. A key difference in the course of the infection between reservoir and spillover hosts is the inflammatory response that either establishes a persistent infection at low cytokine and viral levels or a cytokine storm that results in tissue destruction. In this investigation, we apply a simple model with a small number of parameters to illustrate the local cytokine response to a viral infection that represents several outcomes, two of which are the low level persistence and the cytokine storm. We apply the ordinary differential equation (ODE) model, formulated by Baker et al. (2013), which has only two state variables representative of the functional role played by pro- and anti-inflammatory cytokines. Model parameter values can be interpreted in terms of cytokine agonistic or antagonistic responses. The model provides new insights into the cytokine dynamics. A bifurcation analysis of the dimensionless model demonstrates an array of cytokine dynamical behaviors, from stabilizing at a low concentration, to bi-stable states, to oscillations around a high cytokine levels to relapse-remission flare-ups, and convergence to a high cytokine levels. Two new stochastic differential equation (SDE) models are formulated to account for either local variability in pro- and anti-inflammatory levels or for variability in activation rates. When cytokine concentrations are large, the local variability in the SDE model differs little from the ODE model. However, if external inputs allow for greater variability in activation rates, occasional flare-ups can be seen in the SDE model even if the ODE model exhibits bistability. We interpret the model results in terms viral zoonoses and infection within a natural reservoir or within humans.


The brief introduction to the reporter: Dr. Wenjing Zhang, Assistant Professor in the Department of Mathematics and Statistic at Texas Tech University (TTU). Dr. Zhang is an Applied Mathematician who is interested in dynamical systems and its application in biology. She is studying mechanisms underlying infectious diseases and autoimmune diseases through deterministic and stochastic models. In her studies, deterministic disease dynamics are categorized in parameter spaces through bifurcation theory, more dynamics can appear with stochastic variations. Her work focuses on the recurrent phenomenon in HIV viral blips, relapse-remission pattern in autoimmune diseases, and uncontrolled cytokine flare-ups causing cytokine storms in SARS, Avian influenza, and Hantavirus cardiopulmonary syndrome. Dr. Zhang received her PhD in Applied Mathematics from Western University (University of Western Ontario) in Canada. Before joining TTU she was a Postdoctoral Fellow in the Department of Mathematics and Statistics at York University (Canada).