Michael P. Atkinson

Analyzing the control of mosquito-borne diseases by a dominant lethal genetic system

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 ≈1 year is feasible for affected human populations on the order of 105 to 106, 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.

A Dynamic Model for Posttraumatic Stress Disorder Among U.S. Troops in Operation Iraqi Freedom

We develop a dynamic model in which Operation Iraqi Freedom (OIF) servicemembers incur a random amount of combat stress during each month of deployment, develop posttraumatic stress disorder (PTSD) if their cumulative stress exceeds a servicemember-specific threshold, and then develop symptoms of PTSD after an additional time lag. Using Department of Defense deployment data and Mental Health Advisory Team PTSD survey data to calibrate the model, we predict that---because of the long time lags and the fact that some surveyed servicemembers experience additional combat after being surveyed---the fraction of Army soldiers and Marines who eventually suffer from PTSD will be approximately twice as large as in the raw survey data. We cannot put a confidence interval around this estimate, but there is considerable uncertainty (perhaps ±30%). The estimated PTSD rate translates into ≈300,000 PTSD cases among all Army soldiers and Marines in OIF, with ≈20,000 new cases each year the war is prolonged. The heterogeneity of threshold levels among servicemembers suggests that although multiple deployments raise an individuals risk of PTSD, in aggregate, multiple deployments lower the total number of PTSD cases by ≈30% relative to a hypothetical case in which the war was fought with many more servicemembers (i.e., a draft) deploying only once. The time lag dynamics suggest that, in aggregate, reserve servicemembers show symptoms ≈1--2 years before active servicemembers and predict that >75% of OIF servicemembers who self-reported symptoms during their second deployment were exposed to the PTSD-generating stress during their first deployment.

A novel allocation strategy for blood transfusions: investigating the tradeoff between the age and availability of transfused blood

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.

When Do Armed Revolts Succeed: Lessons from Lanchester Theory

Major revolts have recently erupted in parts of the Middle East with substantial international repercussions. Predicting, coping with and winning those revolts have become a grave problem for many regimes and for world powers. We propose a new model of such revolts that describes their evolution by building on the classic Lanchester theory of combat. The model accounts for the split in the population between those loyal to the regime and those favouring the rebels. We show that, contrary to classical Lanchesterian insights regarding traditional force-on-force engagements, the outcome of a revolt is independent of the initial force sizes; it only depends on the fraction of the population supporting each side and their combat effectiveness. The models predictions are consistent with the situations currently observed in Afghanistan, Libya and Syria (September 2011), and it points to how those situations might evolve.

A Graph Patrol Problem with Random Attack Times

This paper presents a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. To design a patrol policy, the patroller needs to take into account not only the graph structure, but also the different attack time distributions, as well as different costs incurred due to successful attacks, at different nodes. We consider both random attackers and strategic attackers. A random attacker chooses which node to attack according to a probability distribution known to the patroller. A strategic attacker plays a two-person zero-sum game with the patroller. For each case, we give an exact linear program to compute the optimal solution. Because the linear programs quickly become computationally intractable as the problem size grows, we develop index-based heuristics. In the random-attacker case, our heuristic is optimal when there are two nodes, and in a suitably chosen asymptotic regime. In the strategic-attacker case, our heuristic is optimal when there are two nodes if the attack times are deterministic taking integer values. In our numerical experiments, our heuristic typically achieves within 1% of optimality with computation time orders of magnitude less than what is required to compute the optimal policy.

An Overlapping Networks Approach to Resource Allocation for Domestic Counterterrorism

Motivated by the links between terror and crime and the difficulty in directly detecting terror activity, this article formulates and solves a resource allocation problem on overlapping networks to determine if interdiction efforts may be able to take advantage of these connections. The government, knowing only the general structure and overlap of the networks, allocates its scarce resources to investigate each terror and criminal network. There are two stages to the investigation: an initial investigation of all nodes (i.e., terrorists or criminals) and a secondary investigation of criminals identified during the initial investigation to determine if they are terrorists. Applying the model to data derived from a population of terrorists in the United States between 1971–2003 suggests that the government may be able to exploit the terror connections of crimes that are relatively uncommon, somewhat easy to detect, and are attractive to terrorists.

On popular response to violence during insurgencies

Population behavior is a key factor in the evolution and outcome of insurgencies. This behavior is affected by the violence exerted by the insurgents and the regime. In this paper we model the effect of targeted (i.e., coercion) and misguided (i.e., collateral casualties) violence on the behavior of the population. It is shown that excess violence and poor targeting accuracy may lead to situations where a populations support for a certain side will vanish. Copyright 2012 Elsevier B.V. All rights reserved.

Carrots, Sticks and Fog During Insurgencies

We formulate a rational choice model of popular behavior during an insurgency. An individual in the population either supports the insurgents or the government depending upon his attitude and the actions taken by each side. We focus on the effect of insurgency actions: benefits, impositions, and coercion. While benefits and impositions are applied uniformly throughout, the insurgents intend to only coerce those actively providing information to the government. However, due to the “fog of war”, which may lead to limited situational awareness, the insurgents may mistakenly coerce their own supporters and potentially drive them to aid the government. We examine how popular behavior varies under different situational awareness scenarios. When the insurgents have little situational awareness, they should take few coercive actions. This implies that the government will be able to foster intelligence sources within the population. If the insurgents have perfect situational awareness, tipping points may occur that result in a significant reduction in active support for the government. In this case the government should take actions to decrease the coercing effectiveness of the insurgents and increase incentives to the population so they continue to provide information.

When Is Information Sufficient for Action? Search with Unreliable yet Informative Intelligence

We analyze a variant of the whereabouts search problem, in which a searcher looks for a target hiding in one of n possible locations. Unlike in the classic version, our searcher does not pursue the target by actively moving from one location to the next. Instead, the searcher receives a stream of intelligence about the location of the target. At any time, the searcher can engage the location he thinks contains the target or wait for more intelligence. The searcher incurs costs when he engages the wrong location, based on insufficient intelligence, or waits too long in the hopes of gaining better situational awareness, which allows the target to either execute his plot or disappear. We formulate the searcher’s decision as an optimal stopping problem and establish conditions for optimally executing this search-and-interdict mission.

Operating with an incomplete checklist

ABSTRACT We consider a time-critical operation that is contingent on completing a preliminary set of actions in a checklist. Aerial combat missions, emergency surgeries, launching a new product, and rescuing hostages are a few examples of such situations. The operation may be executed before the full checklist is completed but then it may fail. The failure probability depends on the uncompleted actions. The question is when to abort the checklist and initiate the operation. In this article, we study this problem and prove that in certain realistic cases a simple myopic approach is optimal.