Abstract
Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in delayed vaccine deployment, and the interaction between members of different cities facilitates a wide spatial spread of infection. Limited vaccine, time delays, and interaction (or coupling) of cities lead to tradeoffs that impact the overall magnitude of the epidemic. These tradeoffs mandate investigation of optimal strategies that minimize the severity of the epidemic by prioritizing allocation of vaccine to specific subpopulations. We use an SIR model to describe the disease dynamics of an epidemic which breaks out in one city and spreads to another. We solve a master equation to determine the resulting probability distribution of the final epidemic size. We then identify tradeoffs between vaccine, time delay, and coupling, and we determine the optimal vaccination protocols resulting from these tradeoffs.
Highlights
Upon the outbreak of infectious disease, effective and widespread intervention through vaccination is of immediate concern
We examine the spread of infection between two interacting cities linked via implied transportation routes, and we investigate how coupling, vaccine, and time delay contribute to tradeoffs which in turn determine optimal vaccine allocation strategies
In order to explore the temporal dynamics of an epidemic and investigate the effects of intervention methods, we utilize the mathematical framework of the SIR model [4], which has been commonly applied to infectious diseases such as influenza [5], measles [6], and whooping cough [7]
Summary
Upon the outbreak of infectious disease, effective and widespread intervention through vaccination is of immediate concern. Distributing and deploying vaccine relies on numerous logistical or even political factors that can result in delays. The extensive modern network of rapid transportation facilitates the spread of infectious disease between communities. If the resources available are insufficient to fully immunize the entire population, strategically allocating vaccine to specific subpopulations can minimize the spread and severity of infection. The interaction between members of different cities and the time delay until vaccination lead to tradeoffs that can dictate optimal strategies of distributing limited vaccine. Optimizing resource allocation is of great interest to policymakers who must decide who gets vaccinated and when
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