Within-host infectious disease models accommodating cellular coinfection, with an application to influenza

Abstract

Within-host models are useful tools for understanding the processes regulating viral load dynamics. While existing models have considered a wide range of within-host processes, at their core these models have shown remarkable structural similarity. Specifically, the structure of these models generally consider target cells to be either uninfected or infected, with the possibility of accommodating further resolution (e.g. cells that are in an eclipse phase). Recent findings, however, indicate that cellular coinfection is the norm rather than the exception for many viral infectious diseases, and that cells with high multiplicity of infection are present over at least some duration of an infection. The reality of these cellular coinfection dynamics is not accommodated in current within-host models although it may be critical for understanding within-host dynamics. This is particularly the case if multiplicity of infection impacts infected cell phenotypes such as their death rate and their viral production rates. Here, we present a new class of within-host disease models that allow for cellular coinfection in a scalable manner by retaining the low-dimensionality that is a desirable feature of many current within-host models. The models we propose adopt the general structure of epidemiological 'macroparasite' models that allow hosts to be variably infected by parasites such as nematodes and host phenotypes to flexibly depend on parasite burden. Specifically, our within-host models consider target cells as 'hosts' and viral particles as 'macroparasites', and allow viral output and infected cell lifespans, among other phenotypes, to depend on a cell's multiplicity of infection. We show with an application to influenza that these models can be statistically fit to viral load and other within-host data, and demonstrate using model selection approaches that they have the ability to outperform traditional within-host viral dynamic models. Important in vivo quantities such as the mean multiplicity of cellular infection and time-evolving reassortant frequencies can also be quantified in a straightforward manner once these macroparasite models have been parameterized. The within-host model structure we develop here provides a mathematical way forward to address questions related to the roles of cellular coinfection, collective viral interactions, and viral complementation in within-host viral dynamics and evolution.

Keywords: cellular coinfection; influenza virus; macroparasite model; viral complementation; within-host dynamics.

Figure 1.

A schematic showing parallels between epidemiological and within-host infectious disease models. Epidemiological models fall into two groups: (A) models for microparasites and (B) models for macroparasites, such as nematodes. Models for microparasites categorize individuals as being infected or uninfected. Models for macroparasites consider the parasite burden of infected individuals, as this burden affects the production rate of macroparasites from infected hosts and the mortality rate of hosts. (C) General structure of current within-host disease models. These models generally categorize cells as being infected or uninfected. (D) Schematic of a within-host ‘macroparasite’ model, proposed here. Models of this type would consider the multiplicity of cellular infection, as multiplicity of infection affects the rate of viral production and the lifespan of infected cells, among other phenotypes.

Figure 2.

Target-cell limited within-host model dynamics. (A) Within-host viral dynamics, parameterized by fitting target-cell limited models to influenza A/H3N8 viral load measurements from experimentally infected ponies (black circles and x’s). The dashed black line shows the limit of detection, and x markers show below the limit of detection measurements. Colored lines show maximum likelihood fits of the classic within-host target-cell limited microparasite model and of the target-cell limited macroparasite model. (B) The number of target cells over time for the within-host target-cell limited microparasite model (given by T + I) and for the within-host macroparasite model (given by H).

Figure 3.

Dynamics of quantities derived from the target-cell limited within-host macroparasite model. (A) Mean multiplicity of infection (MOI) over time for each of the ponies shown in Fig. 2A. Mean MOI is calculated as the total number of intracellular particles divided by the total number of target cells, P(t)/H(t), where t is time since infection. (B) The proportion of infected cells that are infected by more than one viral particle, calculated from the within-host macroparasite model. (C) The fraction of the viral population that is reassortant, shown over the course of infection.

Figure 4.

Within-host dynamics from the three considered innate immune response models. (A) Model-simulated within-host viral dynamics, with data and limit of detection shown as in Fig. 2A. (B) Model-simulated interferon-α dynamics, along with IFN-α fold change measurements. (C) Model-simulated target cell dynamics. Dashed black line shows an estimate for the final number of target cells, given by a 27 per cent reduction in the number of target cells (Saenz et al. 2010).