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.

The RNA interference (RNAi) drug ARC-520 was shown to be effective in reducing serum hepatitis B virus (HBV) DNA, hepatitis B e antigen (HBeAg) and hepatitis B surface antigen (HBsAg) in HBeAg-positive patients treated with a single dose of ARC-520 and daily nucleosidic analogue (entecavir). To provide insights into HBV dynamics under ARC-520 treatment and its efficacy in blocking HBV DNA, HBsAg, and HBeAg production we developed a multi-compartmental pharmacokinetic–pharamacodynamic model and calibrated it with frequent measured HBV kinetic data. We showed that the time-dependent single dose ARC-520 efficacies in blocking HBsAg and HBeAg are more than 96% effective around day 1, and slowly wane to 50% in 1–4 months. The combined single dose ARC-520 and entecavir effect on HBV DNA was constant over time, with efficacy of more than 99.8%. The observed continuous HBV DNA decline is entecavir mediated, the strong but transient HBsAg and HBeAg decays are ARC-520 mediated. The modeling framework may help assess ongoing RNAi drug development for hepatitis B virus infection.

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The size of primary challenge with lipopolysaccharide induces changes in the innate immune cells phenotype between pro-inflammatory and pro-tolerant states when facing a secondary lipopolysaccharide challenge. To determine the molecular mechanisms governing this differential response, we propose a mathematical model for the interaction between three proteins involved in the immune cell decision making: IRAK-1, PI3K, and RelB. The mutual inhibition of IRAK-1 and PI3K in the model leads to bistable dynamics. By using the levels of RelB as indicative of strength of the immune responses, we connect the size of different primary lipopolysaccharide doses to the differential phenotypical outcomes following a secondary challenge. We further predict under what circumstances the primary LPS dose does not influence the response to a secondary challenge. Our results can be used to guide treatments for patients with either autoimmune disease or compromised immune system.

The observed dynamics of infectious diseases are driven by processes across multiple scales. First is within-host, that is how an infection progresses inside a single individual (for instance viral and immune dynamics). Second 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 wholistic 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 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 19 of 139 qualifying papers across 30 years that include both linked models at the within and between host levels 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.