Manchanda2014 – Modelling infection course induced by four different influenza strains
March 2020, model of the month by Krishna Kumar Tiwari
Original model: BIOMD0000000712
Introduction
Over the years, human population across the globe is devastated by emergence of new viruses or their new stains, causing minor illness (like flu) to major pandemic (like Influenza (caused by H1N1), Zika fever (caused by Zika Virus) or the most recent COVID-19 (caused by Coronavirus)). With the emanation of every new virus or their strain, there is a prodigious need to develop new vaccination strategy and find a novel anti-viral therapy. This makes the study of viral infection mechanism a very necessity to developing therapeutic strategy and mathematical model presents a very promising aid studying viral-host dynamics and finding novel targets 1. Aiming the same, Manchanda et al, 2014 2 developed a small-scale ordinary differential equation based model of Influenza viral dynamics in host based on easily attainable experimental data to explain differences in influenza kinetics induced by different virus strains in mice. The model delineate reasons for mild and severe influenza along with mono and biphasic response of disease. Model simulation predicts that the cause of second peak of biphasic course of infection is inflammation i.e. hosts own body’s response against infection.
Model
The ODE (ordinary differential equation) model of influenza dynamics in mice includes three main dependent variable representing virus pathogenicity, antiviral immune defence (including innate and adaptive immune response), and inflammation due to pro-inflammatory response. Model predicts the clinical score after the infection with four different virus strains (i.e. Jena/5259 (H1N1), Jena/5555(H1N1), Jena/2688(H1N1) and Bakum/1832(H1N2)) and outputs (P,I,D,S values (Figure1A)) is analysed to determine the course of disease progression
Figure 1: Model structure. A. Variable associated with the model are P (pathogen), D (defence), I (inflammation due to proinflammatory response) and S (clinical score- influenza virus induced symptoms). B. Parameters used in the model. Relation between these variables are given in terms of ODE in the literature. Figure recreated based on Manchanda, 2014 2
Results and Conclusion
Model simulated with different parameter (kp, α, and γ) values depicting each strain of virus and results aligned well with the reported literature. For Jena/5258, threshold parameter δ (Figure 1B) is the most sensitive model parameter and kp (Figure 1B) is the second most sensitive. The infection with this strain is defined by the highest clinical score value that is caused not by a high primary pathogenicity (kp=3.23) but by the inflammation (secondary pathogenicity i.e. host immune response to virus) (Figure2, Left Top). Jena/5258 has the maximal kp value of 5.69. Thus, the cause of high clinical score in both infection course is different i.e Jena/5555 causes the high clinical score by a high primary pathogenicity, while Jena/5258 by high secondary inflammation. The parameter α (Figure 1B) called viral infection rate is the next most sensitive parameter for Jena/5258 with biphasic course of infection. Other three virus strains shows monophasic profile (Figure 2). For all four virus strains, the parameter γ, which quantifies the rate of activation of the immune system, is the third (fourth for Jena/5258) most sensitive parameter – after kp and α (and after δ that is only relevant for the strain Jena/5258) (Figure 2, Left and Right bottom).
Figure 2: Simulation output post model fit to the clinical score after infection with four different virus strains (Jena/5555(H1N1), Jena/5555(H1N1), Jena/2688(H1N1) and Bakum/1832(H1N2). In the plotted graph, P is virus pathogenicity, D is antiviral immune defence, I is Inflammation due to pro-inflammatory response and S is Clinical score, a measure of clinical symptoms.
Model parameters kp, α, and γ were the most discriminative and identifiable parameters that quantitatively characterize the four virus strains under investigated in this study. Each of the four virus strains is characterized by a specific pattern with respect to these three parameters (Figure 2).
Discussion
The major aim of the model and simulation was to identify the dynamics of influenza caused by various viral strains based on a single model with limited but most important parameters promising hypothesis for the experimental setup to further explore the driving factor for severe disease and a possible therapy. This small-scale model got some exciting characteristics.
1. it is able to explain the outcome of infection with four influenza virus strains. Thus, the model can be used to quantify the virulence of different strains by a set of 8 parameters listed in Tables 1 and 2 of literature with 4 determining parameters.
2. the model is able to simulate and analyze the cause of different outcomes such as Clinical score of disease after viral infection in mice. Maximum clinical score (Figure 1A) was observed between days 3 and 6 after infection with Jena/5555, Bakum/1832, and Jena/2688; afterwards mice recovered (monophasic kinetic).
Model by Manchanda et al, 2014 2 may help to quantify the dynamics and response of influenza induced by different virus strains and extent support in search for reasons for the severe, biphasic course of infection in mice. The model allows direct antiviral studies including the mathematical analysis of the use of antiviral compounds such as oseltamivir for the treatment of pandemic influenza virus infections (Pitchaimani et al. (2013) 3)
References
1. Carolin Zitzmann and Lars Kaderali 2018. Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling. Front Microbiol. 9, 1546
2. Himanshu Manchanda, Nora Seidelb, Andi Krumbholzb, Andreas Sauerbrei, Michaela Schmidtke, Reinhard Guthke 2014. Within-host influenza dynamics: A small-scale mathematical modeling approach. Biosystems 118, 51-59
3. Pitchaimani, M., Monica, C., Divya, M., 2013. Stability analysis for HIV infection delay model with protease inhibitor. Biosystems 114, 118–124.