Hancioglu2007 - Human immune response to influenza A virus infection

August 2019, model of the month by Jinghao Men
Original model: BIOMD0000000711


Influenza is a common infectious disease caused by the influenza virus. About 3 to 5 million severe cases are estimated every year of which 250,000 to 500,000 cases lead to death [1]. The influenza virus is a negative-single strand RNA enveloped Orthomyxovirus (Baltimore Class V) and it is divided into types A, B, and C, according to the antigenic differences between NP and matrix protein (M). Influenza A viruses (IAV) are subdivided into subtypes such as H1N1, H16N9, etc. based on the antigenic signatures of the major surface proteins HA (Haemagglutinin) and NA (Neuraminidase). Both innate and adaptive immune system of the host respond to IAV infection, with characteristic mediators including interferons(IFN), to promote cellular antivirus response, and antibodies, to primarily reduce viral load by neutralization and opsonization. To study the general pattern of immune response to IAV infection along with the roles and effects of adaptive and innate immunity, Hancioglu et al. (2007) [3] introduced this multi-component mathematical model.

The Model

The authors have constructed a simplified and schematic mathematical ODE model of the dynamics of Influenza A Virus infection and the human immune response to the infection. The model is focused on three fundamental components of the immune response: the interferon, the cellular components of innate immunity and the adaptive immunity, all of which have the common goal of limiting the level of the virus concentration and the damage made to the system. These immune components achieve this goal with different strategies and mechanisms of action: Interferon immunity by removing the substrate that virus needs for reproduction (i.e., the healthy cells), cellular immunity by removing the source of new viruses (i.e., the infected cells), and adaptive immunity by lowering the effective load of the virus. The entities and interactions involved in these models are shown in figure 1. The model includes ten ordinary differential equations expressing the level of cells, antibodies, interferon involved and the dead cells. There are 28 parameters and 26 reactions in this model.

Figure 1

Figure 1. Schematic representation of interactions included in the model.


The authors fitted the parameters obtained from experimental data from previous publications(Marchuk 1991; Bocharov and Romanyukha 1994 etc.). This allowed them to simulate the time-dependent evolution of the model entities after infection. The results are shown in figure 2. The maximum virus load appeared at ca. 5 days post infection, and the condition returned to normal after immune response kicks in. The simulations of the model allowed the comparison of viral loads and damage caused by various levels of the initial viral load, infection rate yhv and initial level of antibody in the host. A simulation of the model on an individual without adaptive immune response is also performed. Some relevant observations are as follows: 1. Higher initial viral load or a higher infection rate results in an earlier peak for viral load and a larger peak damage level 2. Higher initial antibody level in host leads to a lower and later peak damage 3. Failure to develop compatible antibodies results in recurrence of the disease and transition to a chronic state.

Figure 2

Figure 2. Time-courses of the viral load, proportion of respiratory epithelial cells, and the three arms of the immune response for a standard course of the disease. Initially, the viral load is V(0)=0.01, all cells are healthy, levels of APC and interferons are zero, effector cells, plasma cells and antibodies are at their homeostatic levels, and antigenic compatibility S(0)=0.1. Panel at the bottom on the right displays cumulative proportions of types of respiratory epithelial cells: at any given time, below the red curve is the proportion of dead cells, between red and green the proportion of infected cells, between green and blue the proportion of resistant cells, and above blue is the proportion of healthy cells. Figure taken from[3]



The authors presented a simplified model of the virus-host interaction of IAV including both innate and adaptive immunity, and analyzed its mathematical properties. This model could be used to explore the symptoms and clinical behavior in more detail. The viral shedding, severity and length of sickness are not significantly changed with different initial virus levels. The disease peaks appears earlier for larger initial virus level. For sufficiently large initial virus level, the disease becomes severe, with maximum viral load and maximum damage increasing proportionally to the size of the initial load. Analysis has shown that the dynamics is mainly controlled by the level of antibody response rather than innate immunity; conversely, if memory cells cannot produce sufficient antibodies against the virus initially, or cannot improve the antigenic compatibility rapid enough, the viral shedding would relapse, leading to a chronic state. This model can also be further developed by linking infectivity and symptoms to particular components of the model, improved biological fidelity and data calibration. The effects of age and genetic variations can also be included as a distribution of parameters for large scale simulations of antiviral therapy trials in different hosts, and for construction of multi-scale models [2].


  1. World Health Organization. Influenza(seasonal). Fact Sheet No.211, March 2014
  2. Clermont, G., Bartels, J., Kumar, R., Constantine, G., Vodovotz, Y., Chow, C., 2004. In silico design of clinical trials: a method coming of age. Crit. Care Med. 32, 2061-2070. DOI:10.1097/01.CCM.0000142394.28791.C3
  3. Baris Hancioglu, David Swigon, Gilles Clermont, 2007. A dynamical model of human immune response to influenza A virus infection Journal of Theoretical Biology 246 (2007) 70-86. DOI:10.1016/j.jtbi.2006.12.015