Implications of asymptomatic carriers for infectious disease transmission and control

Abstract

For infectious pathogens such as Staphylococcus aureus and Streptococcus pneumoniae, some hosts may carry the pathogen and transmit it to others, yet display no symptoms themselves. These asymptomatic carriers contribute to the spread of disease but go largely undetected and can therefore undermine efforts to control transmission. Understanding the natural history of carriage and its relationship to disease is important for the design of effective interventions to control transmission. Mathematical models of infectious diseases are frequently used to inform decisions about control and should therefore accurately capture the role played by asymptomatic carriers. In practice, incorporating asymptomatic carriers into models is challenging due to the sparsity of direct evidence. This absence of data leads to uncertainty in estimates of model parameters and, more fundamentally, in the selection of an appropriate model structure. To assess the implications of this uncertainty, we systematically reviewed published models of carriage and propose a new model of disease transmission with asymptomatic carriage. Analysis of our model shows how different assumptions about the role of asymptomatic carriers can lead to different conclusions about the transmission and control of disease. Critically, selecting an inappropriate model structure, even when parameters are correctly estimated, may lead to over- or under-estimates of intervention effectiveness. Our results provide a more complete understanding of the role of asymptomatic carriers in transmission and highlight the importance of accurately incorporating carriers into models used to make decisions about disease control.

Keywords: asymptomatic infection; epidemiology; infectious disease control; mathematical modelling; pathogen carriage.

Figure 1.

Categorization of mathematical epidemiological models used to study infectious disease transmission when there are asymptomatic carriers (a list of the associated references is provided in electronic supplementary material, figure S1). Here, C indicates asymptomatic carriers, I symptomatic infectives and S susceptible hosts, while solid arrows indicate state transitions that are common to all models in a category, and broken arrows indicate transitions that are present in at least one but not all models in a category.

Figure 2.

Flow diagram illustrating the structure of the model describing the transmission of a pathogen with both symptomatic and asymptomatic infection in its life cycle. S, susceptible hosts; C, asymptomatic carriers; I, symptomatic infectives; λ(C,I)=β(ηC+I)/N, force of infection; α, proportion of new cases that are symptomatic; ξγ, clearance rate of asymptomatic carriage; γ, clearance rate of symptomatic infections; τ, rate of progression to symptomatic infection; ω, rate of regression to carriage.

Figure 3.

Comparisons between the numbers of individuals in the different host compartments at endemic equilibrium ($\hat{S}$ shown in black, $\hat{C}$ shown in white and $\hat{I}$ shown in grey) in the full model (SICS model) versus the SIS model when the transmission rates and recovery rates from symptomatic infection are fixed between the two models. (a) The overall endemic prevalence is greater in the SIS model ($\hat{P}<{\hat{P}}_{\mathrm{SIS}}$, $\mathcal{A}<1$); (b,c) the overall endemic prevalence is greater in the SICS model ($\hat{P}>{\hat{P}}_{\mathrm{SIS}}$, $\mathcal{A}>1$). In (b), the predicted number of symptomatic cases is greater in the SIS model (${\hat{P}}_{\mathrm{I}}<{\hat{P}}_{\mathrm{SIS}}$, $\eta \mathcal{P}<1$), whereas in (c) the predicted number of symptomatic cases is greater in the SICS model (${\hat{P}}_{\mathrm{I}}>{\hat{P}}_{\mathrm{SIS}}$, $\eta \mathcal{P}>1$). Parameter values are provided in electronic supplementary material, appendix E.

Figure 4.

The total prevalence P calculated using the model accounting for asymptomatic carriers is shown as a function of time t before and after an intervention administered at time t=2000 (indicated by the dashed red line) for two different values of the relative reproduction potential of carriers $\mathcal{A}$ that are greater than unity (dashed-dot line) and less than unity (solid line). Here, the intervention (a) increases the regression rate ω from ω=0.1 to ω=0.3; (b) reduces the progression rate τ from τ=0.06 to τ=0.02; (c) reduces the proportion α of new infections that are symptomatic from α=0.7 to α=0.2. Parameter values are provided in electronic supplementary material, appendix E.