Pandemic controllability: a concept to guide a proportionate and flexible operational response to future influenza pandemics.

The 2009 H1N1 influenza pandemic posed challenges for governments worldwide. Strategies designed to limit community transmission, such as antiviral deployment, were largely ineffective due to both feasibility constraints and the generally mild nature of disease, resulting in incomplete case ascertainment. Reviews of national pandemic plans have identified pandemic impact, primarily linked to measures of transmissibility and severity, as a key concept to incorporate into the next generation of plans. While an assessment of impact provides the rationale under which interventions may be warranted, it does not directly provide an assessment on whether particular interventions may be effective. Such considerations motivate our introduction of the concept of pandemic controllability. For case-targeted interventions, such as antiviral treatment and post-exposure prophylaxis, we identify the visibility and transmissibility of a pandemic as the key drivers of controllability. Taking a case-study approach, we suggest that high-impact pandemics, for which control is most desirable, are likely uncontrollable with case-targeted interventions. Strategies that do not rely on the identification of cases may prove relatively more effective. By introducing a pragmatic framework for relating the assessment of impact to the ability to mitigate an epidemic (controllability), we hope to address a present omission identified in pandemic response plans.

Effective reproduction numbers are commonly overestimated early in a disease outbreak.

Reproduction numbers estimated from disease incidence data can give public health authorities valuable information about the progression and likely size of a disease outbreak. Here, we show that methods for estimating effective reproduction numbers commonly give overestimates early in an outbreak. This is due to many factors including the nature of outbreaks that are used for estimation, incorrectly accounting for imported cases and outbreaks arising in subpopulations with higher transmission rates. Awareness of this bias is necessary to correctly interpret estimates from early disease outbreak data.

Transmissibility of 2009 pandemic influenza A(H1N1) in New Zealand: effective reproduction number and influence of age, ethnicity and importations.

The first wave of pandemic influenza A(H1N1) has subsided in New Zealand as in other southern hemisphere countries. This study aimed to estimate the effective reproduction number (R) of 2009 pandemic influenza A(H1N1) taking into account imported cases. It also aimed to show the temporal variation of R throughout the New Zealand epidemic, changes in age- and ethnicity-specific cumulative incidence, and the effect of school holidays. Using a new modelling method to account for imported cases, we have calculated the peak R during the containment phase of the pandemic as 1.55 (95% confidence interval: 1.16 to 1.86). This value is less than previously estimated in the country early in the pandemic but in line with more recent estimates in other parts of the world. Results also indicated an increase in the proportion of notifications among school-age children after the school holiday (3-19 July 2009). This finding provides support for the potential effectiveness of timely school closures, although such disruptive interventions need to be balanced against the severity of the pandemic.

Modeling thermal burns due to airbag deployment.

Automotive airbags are now a widely accepted safety measure designed to reduce morbidity associated with motor vehicle accidents. Their usage is increasing with multiple airbags (driver, passenger and side curtain) being fitted to many vehicles. However the deployment of airbags has been identified as causing injuries in some instances including minor burns. There are three mechanisms for thermal burns due to an airbag; contact with the hot expelled gases from the airbag, contact with the hot airbag itself and melting of clothing from either of these contacts. A mathematical model is used here to predict the likelihood and severity of the first two types of burns. It is shown that direct contact with high temperature exhaust gases venting from the airbag can indeed lead to burns and that burns from contacting the hot airbag material are possible but far less likely to occur.

Modelling the transmission dynamics of dengue in the presence of Wolbachia.

Use of the bacterium Wolbachia is an innovative new strategy designed to break the cycle of dengue transmission. There are two main mechanisms by which Wolbachia could achieve this: by reducing the level of dengue virus in the mosquito and/or by shortening the host mosquito's lifespan. However, although Wolbachia shortens the lifespan, it also gives a breeding advantage which results in complex population dynamics. This study focuses on the development of a mathematical model to quantify the effect on human dengue cases of introducing Wolbachia into the mosquito population. The model consists of a compartment-based system of first-order differential equations; seasonal forcing in the mosquito population is introduced through the adult mosquito death rate. The analysis focuses on a single dengue outbreak typical of a region with a strong seasonally-varying mosquito population. We found that a significant reduction in human dengue cases can be obtained provided that Wolbachia-carrying mosquitoes persist when competing with mosquitoes without Wolbachia. Furthermore, using the Wolbachia strain WMel reduces the mosquito lifespan by at most 10% and allows them to persist in competition with non-Wolbachia-carrying mosquitoes. Mosquitoes carrying the WMelPop strain, however, are not likely to persist as it reduces the mosquito lifespan by up to 50%. When all other effects of Wolbachia on the mosquito physiology are ignored, cytoplasmic incompatibility alone results in a reduction in the number of human dengue cases. A sensitivity analysis of the parameters in the model shows that the transmission probability, the biting rate and the average adult mosquito death rate are the most important parameters for the outcome of the cumulative proportion of human individuals infected with dengue.

Comparing breastfeeding and breast pumps using a computer model.

There is a role for computer models in increasing the understanding of milk extraction from the human teat. A computer model can be used to investigate aspects of extracting milk from the human teat which are not feasible using clinical experiments. In this paper, the behavior of the human teat during an infant suckling and with the use of a breast pump is modeled. The model is used to (1) identify the role of suction and the peristaltic motion of the tongue during suckling and (2) compare the volume of milk extracted by an infant breastfeeding with that obtained using a breast pump. Infants use a peristaltic motion of the tongue, along with some suction, to extract milk. Breast pumps use a cyclic pattern of suction only. In the model, the human teat is represented as a cylindrical porous elastic material saturated with fluid. We mimic an infant suckling by imposing both suction and a peristaltic force in the computer model of the human teat. This is compared to the effect of suction only, which models the action of breast pumps. The results demonstrate that there is an optimal time to apply the peristaltic force during the suction cycle which will increase the milk volume. The model and results may be of use in the future design of effective breast pumps.

Estimating reproduction numbers for adults and children from case data.

We present a method for estimating reproduction numbers for adults and children from daily onset data, using pandemic influenza A(H1N1) data as a case study. We investigate the impact of different underlying transmission assumptions on our estimates, and identify that asymmetric reproduction matrices are often appropriate. Under-reporting of cases can bias estimates of the reproduction numbers if reporting rates are not equal across the two age groups. However, we demonstrate that the estimate of the higher reproduction number is robust to disproportionate data-thinning. Applying the method to 2009 pandemic influenza H1N1 data from Japan, we demonstrate that the reproduction number for children was considerably higher than that of adults, and that our estimates are insensitive to our choice of reproduction matrix.

Dynamics of human milk extraction: a comparative study of breast feeding and breast pumping.

We describe a mathematical model of the flow and deformation in a human teat. Our aim is to compare the theoretical milk yield during infant breast feeding with that obtained through the use of a breast pump. Infants use a peristaltic motion of the tongue, along with some suction, to extract milk, whereas breast pumps use a cyclic pattern of suction only. Our model is based on quasi-linear poroelasticity whereby the teat is modelled as a cylindrical porous elastic material saturated with fluid. We impose a cyclic axial suction pressure difference across the teat and impose a radial compressive force moving along the teat which mimics infant suckling. This is compared to the case of cyclic and steady pumping only which models the action of breast pumps. The results illustrate that there is an optimal time to apply the compressive force during the suction cycle that will increase the flow rate in our theoretical teat. The model and results may be of use in the future design of effective breast pumps.