Mathematical Modeling of the Lethal Synergism of Coinfecting Pathogens in Respiratory Viral Infections: A Review

Abstract

Influenza A virus (IAV) infections represent a substantial global health challenge and are often accompanied by coinfections involving secondary viruses or bacteria, resulting in increased morbidity and mortality. The clinical impact of coinfections remains poorly understood, with conflicting findings regarding fatality. Isolating the impact of each pathogen and mechanisms of pathogen synergy during coinfections is challenging and further complicated by host and pathogen variability and experimental conditions. Factors such as cytokine dysregulation, immune cell function alterations, mucociliary dysfunction, and changes to the respiratory tract epithelium have been identified as contributors to increased lethality. The relative significance of these factors depends on variables such as pathogen types, infection timing, sequence, and inoculum size. Mathematical biological modeling can play a pivotal role in shedding light on the mechanisms of coinfections. Mathematical modeling enables the quantification of aspects of the intra-host immune response that are difficult to assess experimentally. In this narrative review, we highlight important mechanisms of IAV coinfection with bacterial and viral pathogens and survey mathematical models of coinfection and the insights gained from them. We discuss current challenges and limitations facing coinfection modeling, as well as current trends and future directions toward a complete understanding of coinfection using mathematical modeling and computer simulation.

Keywords: coinfection; immune response; influenza A virus; mathematical modeling.

Figure 1

Simulation of IAV–streptococcus coinfection according to the model in Smith and Smith [85] varying time of secondary infection. Target cells (“T”, panel (A)) that become infected enter an eclipse phase (“I1”, panel (B)), transition to producing IAV (“I2”, panel (C)), and are eventually cleared. IAV (“V”, panel (D)) is administered at time 0. Streptococcus (“P”, panel (E)) is administered at varying times of secondary infection. Time is shown in units of days. The time of secondary infection was uniformly sampled between times 5 and 9 for 1000 replicates. The inset shows colors for the time of secondary infection, from time 5 (“Low”) to time 9 (“High”).

Figure 2

Simulation of IAV–RSV coinfection according to the model in [121] varying the time of secondary IAV infection. Susceptible uninfected cells (“S”, panel (A)) are infected by either IAV (“V1”, panel (G)) or RSV (“V2”, panel (H)), enter an eclipse phase (“E1”, panel (B), for IAV, “E2”, panel (C), for RSV), become productively infectious (“I1”, panel (D), for IAV, “I2”, panel (E), for RSV), and then die (“R”, panel (F)). RSV is administered at time 0. IAV is administered at varying times of secondary infection. Time is shown in units of days. The time of secondary infection was uniformly sampled between times 0 and 2 for 1000 replicates. The inset shows colors for the time of secondary infection, from time 0 (“Low”) to time 2 (“High”).

Figure 3

Two-dimensional, spatial simulation of viral–viral coinfection according to the infection model in Figure 2 [121]. The agent-based multicellular spatial model and model parameters were taken from [139]. The simulation consists of a field of individual cells (“Cells”, top) and two viruses represented as diffusive fields (“Virus 1”, middle, and “Virus 2”, bottom). Susceptible cells are infected by either Virus 1 or Virus 2, enter an eclipse phase (“Virus 1 infected” for Virus 1, “Virus 2 infected” for Virus 2), become productively infectious (“Virus 1 releasing” for Virus 1, “Virus 2 releasing” for Virus 2), and then die (“Dead”). Results are shown for days 0 (left), 1 (left-center), 3 (center), 7 (right-center), and 14 (right). Cell types are shown in the top-right legend. Virus concentrations are shown according to the bottom-right color bar. The simulation was implemented in CompuCell3D [140].