Evolving Network Model: A Novel Approach to Disease Simulation
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2018-05-16
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Abstract
Disease modeling is an important tool in epidemiology. Effective epidemiological models can assist public health workers and policymakers in the development of effective disease prevention strategies and the efficient deployment of resources to inhibit the spread of disease. Expanding the scope of disease modeling techniques is an area of active research in applied mathematics. The two most commonly used modeling techniques are compartmental and agent-based disease models. Infectious diseases are transmitted through human populations by either direct or indirect contact. While for some diseases transmission is possible through indirect modes like airborne transmission, contact with contaminated objects, or insect or animal vectors, the spread of many is only possible through direct human-human contact. The type of contact required to lead to transmission varies widely based on the disease itself; for example influenza can be transmitted by casual contact, whereas HIV can only be spread through exchange of infected body fluids. The underlying biology that governs differences in transmission between different diseases is important to consider when developing disease models. While compartmental models operate under the assumption of homogeneous population mixing, agent-based models can capture the important features of the epidemiological contact network underlying the disease transmission. As a result, compartmental models make more accurate predictions for highly infectious diseases that spread by casual contact, whereas agent-based models provide increased accuracy for diseases that cannot spread through casual contact. Therefore, in many cases, agent-based models are able to model the spread of infectious diseases more accurately; however, their computational intensity makes their use unrealistic for modeling large population sizes. Thus, compartmental and agent-based models offer a trade-off between accuracy and efficiency (i.e. feasibility) in disease simulations.[15]
This project is an effort to create and validate an algorithm for a generating a novel disease model that possesses the network accuracy associated with agent-based models, but maintains some of the efficiency of compartmental models. This new, evolving network model compartmentalizes the majority of the network, while creating contact networks only for infected nodes, instead of for the entire population. As the infection spreads, more of the nodes' contact networks are modeled fully, until ultimately a full agent based network is generated. This method has been shown in preliminary testing to require significantly less computation time than simulating disease spread on full agent-based network models.[10] However, this new modeling technique is not an improvement over previous methods unless it can be shown to model networks as realistically as agent-based models can. Therefore, our goal is to demonstrate the ability of the algorithm for the spread of disease on an evolving network to replicate the desired properties of a target network and thus accurately construct a network. Ultimately, the hope is that this evolving network algorithm will enable us to dynamically model the spread of a newly emerging or re-emerging disease in a human population by accurately representing salient features of the contact network in which disease transmission occurs. Such a model would help equip public health systems to study transmission scenarios and possible response strategies through the use of computer simulations in order to be able to plan for disease outbreaks and respond quickly when necessary.
There are many ways to measure how faithfully the generated network models real populations. Generally, the network properties should converge to the properties of the full network, both as the network evolves into the full agent-based network, and within any subnetwork at timesteps before that. In order to assess how well the algorithm is doing this, two main metrics, average degree and average clustering coefficient, are used. The inputs to the algorithm are a degree distribution and a clustering probability, so the model should generate a network whose properties match these input values; however we would also like it to replicate other properties of the network without explicitly having them as inputs. In order to assess this, other metrics, such as average path length and diameter, will be considered and studied as well. Finally, the algorithm will be tested using properties drawn from real social network data, in order to determine under what conditions it is able to reproduce a network similar to the true network.
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Disease Model, Network, Graph Theory, Epidemiology