Linked within-host and between-host models and data for infectious diseases: a systematic review

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.

Keywords: Between-host; Data-model integration; Infectious disease models; Linking mechanism; Mulit-scale modeling; Pathogen transmission; SIR models; Within-host.

Figure 1. Schematic of survey methodology.

(A) PRISMA flowchart showing the inclusion of papers. “Non-papers” refers to database entries that were figures or codes. (B) Schematic of the screening and evaluation questions used. Dashed lines indicate links between questions that were conditional, that is, answering the second question/box depended on the answers to the earlier question. For example, details on the study properties (Q2.1–Q2.7) and questions from the final screening stage (Q3.1–Q3.3) were only collected for the 195 papers that were retained following the abstract screening stage. Questions in boxes 4–8 were completed for all 24 papers that remained following the final screening stage. Questions are found in Text S1; Responses are found in Tables S1–S8; References to all included papers are found in Text S2; References to all excluded papers are found in Text S3; All recorded data can be found in our Supplemental Data Sets.

Figure 2. Summary of papers considered.

Both included and excluded papers by (A) year of publication, (B) host species, and (C) the reason for exclusion (only for excluded papers). Papers were classified as included (gray), out of scope (orange) or excluded (blue) for (A). “Out of scope” designated papers that literally included the search terms but were not topically related.

Figure 3. Focal host species and infection types for included papers.

(A) Type of infection across host species for included papers as bacterial (gray), fungal (orange), macroparasite (blue), multiple (green), protozoa (yellow), viral (dark blue), or other (red). (B) Modeled transmission route across infection types for included papers as direct contact (gray), indirect contact (orange) or multiple routes (blue).

Figure 4. Types of modeling framework used in included papers.

The x-axis shows the model types used in the within-host part of the model while the y-axis shows the model types used in the between-host model. The dots’ diameter represents how many papers used a particular framework.

Figure 5. Mechanisms used to link between and within-host models together.

The number of included papers that used the each of the (A) within-host linking mechanisms and (B) between-host linking mechanisms to connect the models together.

Figure 6. Role of data in multi-scale modeling efforts.

(A) Scale (within-host, linking, or between-host) at which data was incorporated (orange) in the multi-scale models. Some models used data at more than one level. (B) How the data was incorporated into the models: bottom-up, that is, fitting traits (orange); top-down, that is, fitting states (blue) or both (gray).

Figure 7. Method used in data fitting at each scale.

Three fitting methods were considered: Bayesian inference (gray), least squares (orange), maximum likelihood (blue). All other fitting methods were included under “Other” (green). Different fitting methods could be used in the same papers for different scales.