Abstract
The observed dynamics of infectious diseases are driven by processes across multiple scales. Here we focus on two: within-host, that is, how an infection progresses inside a single individual (for instance viral and immune dynamics), and between-host, that is, how the infection is transmitted between multiple individuals of a host population. The dynamics of each of these may be influenced by the other, particularly across evolutionary time. Thus understanding each of these scales, and the links between them, is necessary for a holistic understanding of the spread of infectious diseases. One approach to combining these scales is through mathematical modeling. We conducted a systematic review of the published literature on multi-scale mathematical models of disease transmission (as defined by combining within-host and between-host scales) to determine the extent to which mathematical models are being used to understand across-scale transmission, and the extent to which these models are being confronted with data. Following the PRISMA guidelines for systematic reviews, we identified 24 of 197 qualifying papers across 30 years that include both linked models at the within and between host scales and that used data to parameterize/calibrate models. We find that the approach that incorporates both modeling with data is under-utilized, if increasing. This highlights the need for better communication and collaboration between modelers and empiricists to build well-calibrated models that both improve understanding and may be used for prediction.
Highlights
In the study of biological systems, phenomena are often observed at multiple scales—from sub-cellular to entire populations
We focused on which host species are modeled, which pathogens are modeled, which types of models are used, how the within-host and between-host dynamics are linked, and at what scale data has been used
We found that it was most common for these models to describe a human population, to model a viral disease, to use a deterministic model at either of the two scales considered, to link the pathogen load at the within-host scale, to link the transmission rate at the between-host scale, and to use data at the within-host scale
Summary
In the study of biological systems, phenomena are often observed at multiple scales—from sub-cellular to entire populations. We focus on the between-host scale and the within-host scale, given their frequent appearance as a dichotomy in the study of infectious disease (Mideo, Alizon & Day, 2008; Handel & Rohani, 2015; Willem et al, 2017). Mathematical and computational modeling, which has a rich history of application to the dynamics of ecological systems and infectious diseases, has been used to study phenomena at both within-host and between-host scales (as well as other scales as is reviewed in Garira (2017)). At the between-host scale, classic compartmental models, like the SIR model, which represents the interactions between susceptible individuals S, infected individuals I, and recovered individuals R, have been used to predict the spread of infectious diseases between individuals in a population (Kermack & McKendrick, 1991, 1927; Anderson & May, 1992). At the within-host scale, models such as the TIV model of viral dynamics, which represents the interactions between target cells T, infected cells I, and virus V, have been used to understand viral load within hosts (Perelson et al, 1996; Nowak & May, 2000)
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