A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead

Abstract

Most mathematical models used to study the dynamics of influenza A have thus far focused on the between-host population level, with the aim to inform public health decisions regarding issues such as drug and social distancing intervention strategies, antiviral stockpiling or vaccine distribution. Here, we investigate mathematical modeling of influenza infection spread at a different scale; namely that occurring within an individual host or a cell culture. We review the models that have been developed in the last decades and discuss their contributions to our understanding of the dynamics of influenza infections. We review kinetic parameters (e.g., viral clearance rate, lifespan of infected cells) and values obtained through fitting mathematical models, and contrast them with values obtained directly from experiments. We explore the symbiotic role of mathematical models and experimental assays in improving our quantitative understanding of influenza infection dynamics. We also discuss the challenges in developing better, more comprehensive models for the course of influenza infections within a host or cell culture. Finally, we explain the contributions of such modeling efforts to important public health issues, and suggest future modeling studies that can help to address additional questions relevant to public health.

Figure 1

Course of an influenza infection within a host. The timings of the adaptive immune response, namely Antibodies (Abs) and cytotoxic T lymphocytes (CTL), for both a primary (PR) and secondary (SR) response to an influenza infection are indicated.

Figure 2

Typical kinetics exhibited by the target-cell limited model with a latent phase predicting the course of an influenza infection within a host. We can see that the target cells (T) are consumed rapidly, with viral titer (V ) peaking shortly thereafter. In this picture, there is approximately a 3.6 h delay between the infectious (I) cells’ peak and that of viral titer. The parameters, (β, k, δ, p, c) = (3.2 × 10^-5 ([V] · d)^-1, 4.0 d^-1, 5.2 d^-1, 4.6 × 10^-2 [V]/d,5.2 d^-1), and initial conditions, (T, E, I, V )_t=0 = (4 × 10⁸, 0, 0,7.5 × 10² [V]), where [V] is TCID₅₀/mL of nasal wash are from Table 3 of [15].