Force of infection: a determinant of vaccine efficacy?

Abstract

Vaccine efficacy (VE) can vary in different settings. Of the many proposed setting-dependent determinants of VE, force of infection (FoI) stands out as one of the most direct, proximate, and actionable. As highlighted by the COVID-19 pandemic, modifying FoI through non-pharmaceutical interventions (NPIs) use can significantly contribute to controlling transmission and reducing disease incidence and severity absent highly effective pharmaceutical interventions, such as vaccines. Given that NPIs reduce the FoI, the question arises as to if and to what degree FoI, and by extension NPIs, can modify VE, and more practically, as vaccines become available for a pathogen, whether and which NPIs should continue to be used in conjunction with vaccines to optimize controlling transmission and reducing disease incidence and severity.

Fig. 1. Vaccine Efficacy (VE) as a function of force of Infection (FoI) for hypothetical vaccine.

Equations that define three mathematical scenarios (see Box 2, Vaccine efficacy as a function of force of infection) are shown graphically, using as an example a hypothetical vaccine with a maximum vaccine efficacy (VE_max) of 83.0% and minimum VE (VE_min) of 44.0% studied under conditions of force of infection (FoI) that vary across two orders of magnitude, from a minimum FoI (FoI_min) 0.03 to a maximum FoI (FoI_max) of 3.50 infections/person-year.

Fig. 2. Vaccine Efficacy (VE) as a function of Force of Infection (FoI) for malaria vaccine.

Best fit trendline analysis of observed vaccine efficacy (VE_observed) as a function of observed force of infection (FoI_observed) is shown as a logarithmic relationship (blue dotted line) with a R² of 0.807. A regression analysis of VE_observed as a function of ln FoI_observed shown in the embedded table has a Significance F of 0.006. Using the VE_{natural log} equation (see Box 2, Vaccine efficacy as a function of force of infection), the observed VE_max, VE_min, FoI_max, FoI_min, and FoI_observed were used to calculate the VE_{natural log} in the embedded table and the calculated VE_{natural log} shown graphically (orange dotted line).

Fig. 3. Vaccine Efficacy (VE) as a function of Force of Infection (FoI) for rotavirus vaccines.

a RV1: Best fit trendline analysis of observed vaccine efficacy (VE_observed) as a function of observed force of infection (FoI_observed) is shown as a linear relationship for all 10 countries (blue dotted line) and for 9 countries (exclusion of the outlier, encircled blue dot; gray dotted line) with a R² of 0.3892 and 0.6264, respectively. Regression analyses of VE_observed as a function of FoI_observed in the embedded table have Significance Fs of 0.158 and 0.0449. Using the VE_linear equation (see Box 2, Vaccine efficacy as a function of force of infection), the observed VE_max, VE_min, FoI_max, FOI_min and FoI_observed were used to calculate the VE_linear in the embedded table and the calculated VE_linear shown graphically (orange dotted line). b RV5: Best fit trendline analysis of observed vaccine efficacy (VE_observed) as a function of observed force of infection (FoI_observed) is shown as a linear relationship (blue dotted line) with a R² of 0.6692. A regression analysis of VE_observed as a function of FoI_observed in the embedded table has a Significance F of 0.081. Using the VE_linear equation (see Box 2, Vaccine efficacy as a function of force of infection), the observed VE_max, VE_min, FoI_max, FOI_min and FoI_observed were used to calculate the VE_linear in the embedded table and the calculated VE_linear shown graphically (orange dotted line).