Mathematical Modeling and Analysis of Influenza In-Host Infection Dynamics

Abstract

Influenza is a viral infectious disease of high importance widely studied around the world. In this study we model within-host transmission of influenza in a continuous deterministic setting, a discrete stochastic framework and a spatial-temporal model. Previous models omit cellular restoration through cellular death, which is a key component for the possibility of chronic infections. We thus investigate the effect of cellular restoration on the spread of influenza within the host, through stability analysis of the deterministic model, the probability of state transitions in the stochastic model and the effect of mobility rates on disease spread in the spatial-temporal model. Using the Partial Rank Correlation Coefficient and the Latin Hypercube Sampling, we performed sensitivity analysis to determine which of the parameters are most influential to the model output.