Modeling Influenza Virus Infection: A Roadmap for Influenza Research

Abstract

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization.

Keywords: aging; coinfection; host genetic factors; influenza; mathematical models; parameters estimation; vaccinology.

Figure 1

Influenza A virus (IAV) infection and dynamics. (a) Description of the main phases of IAV infection within a host. After entering the respiratory tract, each virion binds to a target cell. Then, virions enter the eclipse phase (5–12 hpi), before starting to replicate and infecting other cells; (b) IAV and immune response (IR) dynamics. The innate IR is mainly represented by interferon (IFN)-I and by natural killer (NK) cells, whereas the adaptive IR is mainly driven by cytotoxic CD8${}^{+}$ T cells (CTLs) and antibodies (Abs). Days post infection is abbreviated with dpi.

Figure 2

Target cell model. (Left) IAV (V) infects susceptible cells (U) with rate β. Infected cells are cleared with rate δ. Once cells are productively infected (I), they release virus at rate p and virus particles are cleared at rate c. The symbol ϕ represents clearance; (Right) Computational simulations of the target cell model. Parameter values used for model simulation are taken from [26]. The susceptible cells (red line) are rapidly infected while the virus (black line) and infected cells (blue line) peak at day one approximately. The viral growth is limited by the number of susceptible cells, decreasing the viral load and the number of infected cells to undetectable levels.

Figure 3

Mathematical modeling approach. From an experimental data set available, a mathematical model is developed/applied (step 1); Then, the identifiability analysis (step 2) should be carried out; Then, parameter uncertainty (step 3) is evaluated providing parameter confidence intervals. In this phase scatter plots can inform on the parameters relation and their influence on the mathematical model; Once reasonable parameter values are obtained, model prediction (step 4) can be performed generating new knowledge on the biological process and testing different scenarios.

Figure 4

Viral infection model with CTLs response. IAV (V) induces CTLs (E) clonal expansion with a rate r which inhibits the viral replication through the clearance of the infected cell, this effect can be included in ${\text{c}}_{\text{v}}$. CTLs are replenished with rate ${\text{s}}_{\text{E}}$ and die with rate ${\text{c}}_{\text{e}}$.

Figure 5

Profile likelihood for the model parameters. (a) p is the viral replication rate; (b) ${\text{c}}_{\text{v}}$ represents the viral clearance; (c) ${\text{k}}_{\text{e}}$ is the CTLs half saturation constant; (d) r represents the CTLs proliferation rate.

Figure 6

Viral infection model fitting: (a) The model fitting is shown with a blue line, viral load data is presented in red squares for mice infected with the IAV (H1N1) (PR8) strain; (b) the model fitting is shown in a blue line, the CTLs data is presented in red squares.

Figure 7

Nonparametric bootstrap results. The distributions of the nonparametric bootstrap obtained with 1000 samples for the model parameters (a) p; (b) ${\text{c}}_{\text{v}}$; (c) ${\text{k}}_{\text{e}}$; (d) r.

Figure 8

Scatter plot results. The scatter plots of (a) p-${\text{c}}_{\text{v}}$; (b) ${\text{k}}_{\text{e}}$-r; (c) ${\text{k}}_{\text{e}}$-p; (d) r-p; (e) r-${\text{c}}_{\text{v}}$, (f) ${\text{k}}_{\text{e}}$-${\text{c}}_{\text{v}}$. The numerical values are obtained from the nonparametric bootstrap distributions in Figure 7. The plots show dependencies between parameters p-${\text{c}}_{\text{v}}$, p-r, ${\text{c}}_{\text{v}}$-r.

Figure 9

Main challenges in IAV infection. IAV infections facilitate secondary bacterial infections impairing the IR deputed to the bacterial clearance. The IAV infection is controlled by IR, which in turn is shaped by host genetic factors, previous infections, vaccination, and aging.

Figure 10

Emerging vaccination strategies. Novel vaccination strategies can for example (i) enhance mucosal IR against IAV reducing horizontal transmission and virus spread; (ii) display improved efficacy in poor responders such as elderly. Novel technologies will enable rapid production of emerging virus strains (e.g., synthetic mRNA or RNA replicon based vaccines) or universal vaccines covering major clades (e.g., designed hemagglutinins triggering broad neutralizing antibodies or vaccines triggering cross-protective CTL responses).