Motivated by the desire to assess nonpharmaceutical interventions for pandemic influenza, we seek in this study to quantify the routes of transmission for this disease. We construct a mathematical model of aerosol (i.e., droplet-nuclei) and contact transmission of influenza within a household containing one infected. An analysis of this model in conjunction with influenza and rhinovirus data suggests that aerosol transmission is far more dominant than contact transmission for influenza. We also consider a separate model of a close expiratory event, and find that a close cough is unlikely ( approximately 1% probability) to generate traditional droplet transmission (i.e., direct deposition on the mucous membranes), although a close, unprotected and horizontally-directed sneeze is potent enough to cause droplet transmission. There are insufficient data on the frequency of close expiratory events to assess the relative importance of aerosol transmission and droplet transmission, and it is prudent to leave open the possibility that droplet transmission is important until proven otherwise. However, the rarity of close, unprotected and horizontally-directed sneezes-coupled with the evidence of significant aerosol and contact transmission for rhinovirus and our comparison of hazard rates for rhinovirus and influenza-leads us to suspect that aerosol transmission is the dominant mode of transmission for influenza.

Motivated by the failure of current methods to control dengue fever, we formulate a mathematical model to assess the impact on the spread of a mosquito-borne viral disease of a strategy that releases adult male insects homozygous for a dominant, repressible, lethal genetic trait. A dynamic model for the female adult mosquito population, which incorporates the competition for female mating between released mosquitoes and wild mosquitoes, density-dependent competition during the larval stage, and realization of the lethal trait either before or after the larval stage, is embedded into a susceptible-exposed-infectious-susceptible human-vector epidemic model for the spread of the disease. For the special case in which the number of released mosquitoes is maintained in a fixed proportion to the number of adult female mosquitoes at each point in time, we derive mathematical formulas for the disease eradication condition and the approximate number of released mosquitoes necessary for eradication. Numerical results using data for dengue fever suggest that the proportional policy outperforms a release policy in which the released mosquito population is held constant, and that eradication in Ϸ1 year is feasible for affected human populations on the order of 10 5 to 10 6 , although the logistical considerations are daunting. We also construct a policy that achieves an exponential decay in the female mosquito population; this policy releases approximately the same number of mosquitoes as the proportional policy but achieves eradication nearly twice as fast.dengue fever ͉ genetically modified mosquitoes ͉ mathematical epidemiology W orldwide morbidity and mortality from mosquito-borne viral diseases are substantial and on the rise (1). No licensed vaccine exists for the most important of these viruses, the dengue virus, which each year causes 50-100 million cases of dengue fever and 250,000-500,000 cases of the potentially fatal dengue hemorrhagic fever (2). The Aedes aegypti mosquito (also known as Stegomyia aegypti), which is the main vector for dengue fever and yellow fever, is endemic in the southeastern U.S., and the West Nile virus spread easily through the U.S. in recent years, suggesting the U.S. could be vulnerable in coming years to both natural and deliberate outbreaks of mosquito-borne viral diseases. Given the failure of current methods to control the spread of these diseases, considerable effort has gone into novel population-suppression strategies. The sterile insect technique (SIT), which releases sterile (irradiated) male insects that mate with wild females, resulting in no progeny, has been used successfully for Ͼ50 years for control and eradication of several pests and disease vectors (3, 4). However, irradiated mosquitoes have difficulty competing with wild males for wild females (5-7) and there are no large-scale SIT mosquito programs currently in operation. A proposed alternative approach that is also environmentally benign is the release of insects carrying a dominant lethal (RIDL) strategy. In this ap...

We construct a mathematical model of aerosol (i.e., droplet-nuclei) transmission of influenza within a household containing one infected and embed it into an epidemic households model in which infecteds occasionally infect someone from another household; in a companion paper, we argue that the contribution from contact transmission is trivial for influenza and the contribution from droplet transmission is likely to be small. Our model predicts that the key infection control measure is the use of N95 respirators, and that the combination of respirators, humidifiers, and ventilation reduces the threshold parameter (which dictates whether or not an epidemic breaks out) by approximately 20% if 70% of households comply, and by approximately 40% if 70% of households and workplaces comply (approximately 28% reduction would have been required to control the 1918 pandemic). However, only approximately 30% of the benefits in the household are achieved if these interventions are used only after the infected develops symptoms. It is also important for people to sleep in separate bedrooms throughout the pandemic, space permitting. Surgical masks with a device (e.g., nylon hosiery) to reduce face-seal leakage are a reasonable alternative to N95 respirators if the latter are in short supply.

We formulate and solve an optimization problem in which a terrorist is attempting to drive a nuclear weapon toward a city center, but needs to travel through an array of imperfect neutron radiation sensors that form a wall around the periphery of the city. A fleet of interdiction vehicles are available to chase, and attempt to interdict, vehicles that set off a sensor alarm. In our model, the government chooses the thickness (in terms of number of sensors) of the radiation wall, the neutron threshold in the sensors, and the number of interdiction vehicles to minimize the expected damage inflicted by a terrorist, subject to a budget constraint on sensors and interdiction vehicles. The terrorist observes the wall thickness and at each node he updates his likelihood of passing through a sensor without triggering an alarm and decides whether to proceed through the sensor or stop and detonate the bomb. Our results suggest that for an annual cost ranging from several million dollars to several tens of millions of dollars, depending upon the city's roadway topology, a single layer of sensors placed tens of miles from the city center and 10-20 dedicated interdiction vehicles could mitigate the damage from an unshielded or lightly-shielded plutonium weapon, but not from a uranium weapon or a radiological dispersal device.

BACKGROUND:Recent studies show that transfusing older blood may lead to increased mortality. This raises the issue of whether transfusing fresher blood can be achieved without jeopardizing blood availability. STUDY DESIGN AND METHODS:We propose a simple family of policies that is defined by a single threshold: rather than transfusing the oldest available blood that is younger than 42 days, we transfuse the oldest blood that is younger than the threshold, and if there is no blood younger than the threshold then we transfuse the youngest blood that is older than the threshold. To assess this policy, we build a simulation model using data from Stanford University Medical Center. We focus on the tradeoff between the mean age of transfused blood and the fraction of transfused blood that is imported. RESULTS: For hospitals in which the local supply is greater than demand, our policy with a threshold of 14 days leads to a decrease of 10 to 20 days in the mean age of transfused blood while increasing the fraction of imported blood to less than 0.005 (i.e., 0.5%). If the health benefits from transfusing fresher blood can be confirmed by randomized clinical trials, then conservative assumptions suggest that this policy could reduce the annual number of transfused patients who die within 1 year by 20,000. CONCLUSION: The proposed allocation policy with a threshold of 14 days could allow many US hospitals to significantly reduce the age of transfused blood, thereby possibly reducing morbidity and mortality, while having a negligible impact on supply chain operations.