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Local Analysis of Individual-based Viral Dynamic Models with Eigenspace and Eigenvalue Elasticity Analysis

Eigenvalue elasticity methods have been widely applied in analyzing linear and simple nonlinear systems. In this study, we applied this approach to gain insight into the leverage offered by parameter changes in individual-based viral dynamic models for studying and controlling infectious disease spread. We found that such eigenspace based methods encounter severe limitations when applied to nonlinear systems with a relatively large number of state variables. Although eigenvalue elasticity offers some insight into the short-term impact of parameter changes, eigenvalue elasticity method can be complicated and even unwieldy for understanding the impacts of parameter changes for models with a relatively large number of state variables because of eigenvalue multiplicity, co-effects of eigenvalues, eigenvectors and coefficients. In terms of disease control, while such analysis methods could be helpful for identifying policy levers with high short-term impact, it is inefficient. In addition, we found that parameter changes guided by such local techniques are usually insufficient to alter system behaviors in the long-term, such as in the phase of endemic spread in the infectious disease spread. We argue that further work should be focused on refining eigenspace techniques and developing global analysis method to understand the impact of parameter changes on long-term behavior.