Schematics depicting the mechanistic actions of each vaccine.

Across all panels, yellow shaded individuals correspond to infectious cases with mild symptoms, red shaded individuals correspond to infectious cases with severe symptoms, blue shaded individuals correspond to those who are vaccinated. The values on the arrows show the corresponding probability. The three vaccines displayed are: (A) symptom-attenuating vaccine—an infected individual who is vaccinated had a probability η of having mild disease, and a probability 1 − η of their symptom severity being determined as usual; (B) an infection-blocking vaccine—a vaccinated individual had a probability η of their infection being prevented, and a probability 1 − η of being infected and their symptom severity being determined as usual; and (C) an infection-blocking vaccine that only admits mild breakthrough infections—a vaccinated individual had a probability η of their infection being prevented, and a probability 1 − η of being infected but only with mild disease.</p

Schematic showing how symptom severity was determined according to the two symptom severity associated parameters, <i>α</i> and <i>ν</i>.

White shaded individuals correspond to those susceptible to infection, yellow shaded individuals correspond to infectious cases with mild severity and red shaded individuals correspond to infectious cases with severe symptoms. The values on the arrows show the corresponding probability. In brief, an infected individual has probability α of copying the symptom severity of their infector and a probability 1 − α of reverting to the baseline probability of having severe disease, i.e. they developed severe disease with probability ν.</p

Supporting information for ‘Epidemiological and health economic implications of symptom propagation in respiratory pathogens: A mathematical modelling investigation’.

This supplement consists of the following parts: (1) Methods for calculating R0 and β; (2) Results with fixed β; (3) Parameterisation details of the health economic model; (4) Results for an alternative vaccine action; (5) Additional epidemiological results; (6) Sensitivity to discounting; (7) Sensitivity to intervention efficacy; (8) Additional health economic findings. (PDF)</p

The relative effectiveness in reducing severe cases of a symptom-attenuating and infection-blocking vaccine as a function of <i>α</i> and <i>ν</i>, given a fixed efficacy (70%).

Rows correspond to the two vaccine uptake levels (A-C) 50%; (D-F) 90%, and columns to the different disease parameterisations ((A,D) seasonal influenza; (B,E) pandemic influenza; (C,F) SARS-CoV-2). Pixel shading denotes (for given combinations of α-ν values) the difference in the proportion of the population severely infected between vaccine types, such that blue regions show parameter combinations where the infection-blocking vaccine was more effective at reducing the number of severe cases and red regions show those where the symptom-attenuating vaccine was more effective.</p

Description of parameters used in the health economic modelling.

(Top) Values applied to both the seasonal influenza and pandemic influenza disease parameterisations. (Bottom) Values applied to the SARS-CoV-2 disease parameterisation.</p

Epidemiological parameter values for the (seasonal and pandemic) influenza and SARS-CoV-2 scenarios.

In each parameterisation, we calibrated the β value to acquire the stated value of R0 in the respective scenario. All rates have a unit of ‘per day’ (day−1). (Top) Parameters used for the two influenza scenarios: influenza-like parameters with R0 = 1.5 (seasonal influenza parameterisation), influenza-like parameters with R0 = 3.0 (pandemic influenza parameterisation). (Bottom) SARS-CoV-2-like parameters with R0 = 3.0.</p

Variation of the threshold unit intervention cost with vaccine uptake.

We normalised threshold unit intervention costs for each disease parameterisation; the normalisation constant was the highest absolute threshold unit intervention cost attained for the respective disease parameterisation across the range of tested uptake values. The three rows correspond to the three different disease parameterisations: (A-C) seasonal influenza; (D-F) pandemic influenza; (G-I) SARS-CoV-2. The three columns correspond to: (A,D,G) a symptom-attenuating vaccine (SA), (B,E,H) an infection-blocking vaccine (IB) and (C,F,I) an infection-blocking vaccine that only admits mild breakthrough infections (IB_MB). The two lines correspond to two symptom propagation strengths; the dashed, light purple line corresponds to α = 0.2 and the solid, dark purple line corresponds to α = 0.8. We fixed the vaccine efficacy at 70% and all other parameters values were as given in Table 1, with ν chosen to fix the proportion of cases that were severe equal to 0.8.</p

Threshold unit intervention cost for the three types of vaccine, two vaccine uptake levels and the three disease parameterisations.

In all panels, we normalised threshold intervention costs by the highest absolute threshold unit intervention cost obtained across the range of tested vaccine uptake values. The three groups of bars correspond to: a symptom-attenuating vaccine (SA), an infection-blocking vaccine (IB) and an infection-blocking vaccine which only admits mild breakthrough infections (IB_MB). The two bars in each group correspond to symptom propagation strengths of α = 0.2 (left bar, hatched lines) and α = 0.8 (right bar, solid fill). The two rows correspond to two vaccine uptake levels: (A-C) 50%; (D-F) 90%. Columns correspond to differing disease parameterisations: (A,D) seasonal influenza; (B,E) pandemic influenza; (C,F) SARS-CoV-2. Vaccine efficacy was fixed at 70% and all other parameters were as given in Table 1, with ν chosen to fix the proportion of cases that were severe equal to 0.8.</p

The proportion of infections that were severe against changes in <i>α</i> and <i>ν</i> for three parameter sets.

The shading shows the proportion of infections that were severe, with darker shading corresponding to a higher proportion being severe. Black lines correspond to the contours taking values from 0.1 to 0.9, at increments of 0.1. The three disease parameterisations used were: (A) Seasonal influenza; (B) Pandemic influenza; (C) SARS-CoV-2. The parameters were as given in Table 1.</p

The final outbreak size, peak prevalence and outbreak duration, by severity, for three disease parameterisations, plotted for different symptom propagation strengths, <i>α</i>.

(A-C) Final outbreak size by severity. (D-F) Peak prevalence by severity. The intensity of the shading denotes the symptom severity class, with severe cases in red and mild cases in yellow. (G-I) Outbreak duration (note the different y-axis scales). In all panels, ν = 0.2. The three disease parameterisations used were: (A,D,G) Seasonal influenza; (B,E,H) Pandemic influenza; (C,F,I) SARS-CoV-2, with parameters as given in Table 1.</p