Optimal vaccine allocation to control epidemic outbreaks in arbitrary networks (original) (raw)

Optimising control of disease spread on networks

Acta Physica Polonica B, 2005

We consider models for control of epidemics on local, global, small-world and scale-free networks, with only partial information accessible about the status of individuals and their connections. The effectiveness of local (e.g. ring vaccination or culling) vs global (e.g. random vaccination) control measures is evaluated, with the aim of minimising the total cost of an epidemic. The costs include direct costs of treating infected individuals as well as costs of treatment. We first consider a random (global) vaccination strategy designed to stop any potential outbreak. We show that if the costs of the preventive vaccination are ignored, the optimal strategy is to vaccinate the whole population, although most of the resources are wasted on preventing a small number of cases. If the vaccination costs are included, or if a local strategy (within a certain neighbourhood of a symptomatic individual) is chosen, there is an optimum number of treated individuals. Inclusion of non-local contacts ('small-worlds' or scale-free networks) increases the levels of preventive (random) vaccination and radius of local treatment necessary for stopping the outbreak at a minimal cost. The number of initial foci also influences our choice of optimal strategy. The size of epidemics and the number of treated individuals increase for outbreaks that are initiated from a larger number of initial foci, but the optimal radius of local control actually decreases. The results are important for designing control strategies based on cost effectiveness.

Optimal curing policy for epidemic spreading over a community network with heterogeneous population

Journal of Complex Networks

The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of allocating recovery resources among the population, at the lowest cost possible to prevent the epidemic from persisting indefinitely in the network. Specifically, we analyze a susceptible-infected-susceptible epidemic process spreading over a weighted graph, by means of a firstorder mean-field approximation. First, we describe the influence of the contact network on the dynamics of the epidemics among a heterogeneous population, that is possibly divided into communities. For the case of a community network, our investigation relies on the graph-theoretical notion of equitable partition; we show that the epidemic threshold, a key measure of the network robustness against epidemic spreading, can be determined using a lower-dimensional dynamical system. Exploiting the computation of the epidemic threshold, we determine a cost-optimal curing policy by solving a convex minimization problem, which possesses a reduced dimension in the case of a community network. Lastly, we consider a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.

Data-driven allocation of vaccines for controlling epidemic outbreaks

We propose a mathematical framework, based on conic geometric programming, to control a susceptible-infectedsusceptible viral spreading process taking place in a directed contact network with unknown contact rates. We assume that we have access to time series data describing the evolution of the spreading process observed by a collection of sensor nodes over a finite time interval. We propose a data-driven robust convex optimization framework to find the optimal allocation of protection resources (e.g., vaccines and/or antidotes) to eradicate the viral spread at the fastest possible rate. In contrast to current network identification heuristics, in which a single network is identified to explain the observed data, we use available data to define an uncertainty set containing all networks that are coherent with empirical observations. Our characterization of this uncertainty set of networks is tractable in the context of conic geometric programming, recently proposed by Chandrasekaran and Shah [1], which allows us to efficiently find the optimal allocation of resources to control the worst-case spread that can take place in the uncertainty set of networks. We illustrate our approach in a transportation network from which we collect partial data about the dynamics of a hypothetical epidemic outbreak over a finite period of time.

Optimal resource allocation for competing epidemics over arbitrary networks

2015 American Control Conference (ACC), 2015

This paper studies an SI1SI2S spreading model of two competing behaviors over a bilayer network. In particular, we address the problem of determining resource allocation strategies that ensure the extinction of one behavior while not necessarily ensuring the extinction of the other, and pose a marketing problem in which such a model can be of use. Our discussion begins by extending the SI1SI2S model to nodedependent infection and recovery parameters and generalized graph topologies, contrasting prior work. We then find conditions under which a chosen epidemic becomes extinct. We show that a distribution of resources which realizes this goal always exists for some budget under mild assumptions. We address the case in which the available budget is not sufficient for extinction by establishing analytic means for mitigating the spreading rate of the unwanted behavior. We demonstrate a method for tractably computing solutions to each problem via geometric programming. Our results are validated through simulation.

Optimal resource allocation for containing epidemics on time-varying networks

2015 49th Asilomar Conference on Signals, Systems and Computers, 2015

This paper studies the Susceptible-Infected-Susceptible (SIS) epidemic model on time-varying interaction graphs in contrast to the majority of other works which only consider static graphs. After presenting the mean-field model and characterizing its stability properties, we formulate and solve an optimal resource allocation problem. More specifically, we first assume that a cost can be paid to reduce the amount of interactions certain nodes can have with others (e.g., by imposing travel restrictions between certain cities). Then, given a budget, we are interested in optimally allocating the budget to best combat the undesired epidemic. We show how this problem can be equivalently formulated as a geometric program and solved in polynomial time. Simulations illustrate our results.

A method for reducing the severity of epidemics by allocating vaccines according to centrality

Proceedings of the 5th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics - BCB '14, 2014

One long-standing question in epidemiological research is how best to allocate limited amounts of vaccine or similar preventative measures in order to minimize the severity of an epidemic. Much of the literature on the problem of vaccine allocation has focused on influenza epidemics and used mathematical models of epidemic spread to determine the effectiveness of proposed methods. Our work applies computational models of epidemics to the problem of geographically allocating a limited number of vaccines within several Texas counties. We developed a graph-based, stochastic model for epidemics that is based on the SEIR model, and tested vaccine allocation methods based on multiple centrality measures. This approach provides an alternative method for addressing the vaccine allocation problem, which can be combined with more conventional approaches to yield more effective epidemic suppression strategies. We found that allocation methods based on in-degree and inverse betweenness centralities tended to be the most effective at containing epidemics.

Heterogeneous SIS model for directed networks and optimal immunization

ArXiv, 2016

We investigate the influence of a contact network structure over the spread of epidemics in an heterogeneous population. Basically the epidemics spreads over a directed weighted graph. We describe the epidemic process as a continuous-time individual-based susceptible–infected–suscepti-ble (SIS) model using a first-order mean-field approximation. First we consider a network without a specific topology, investigating the epidemic threshold and the stability properties of the system. Then we analyze the case of a community network, relying on the graph-theoretical notion of equitable partition, and using a lower-dimensional dynamical system in order to individuate the epidemic threshold. Moreover we prove that the positive steady-state of the original system, that appears above the threshold, can be computed by this lower-dimensional system. In the second part of the paper we treat the important issue of the infectious disease control. Taking into account the connectivity of the networ...

Outbreak minimization v.s. influence maximization: an optimization framework

BMC Medical Informatics and Decision Making

Background An effective approach to containing epidemic outbreaks (e.g., COVID-19) is targeted immunization, which involves identifying “super spreaders” who play a key role in spreading disease over human contact networks. The ultimate goal of targeted immunization and other disease control strategies is to minimize the impact of outbreaks. It shares similarity with the famous influence maximization problem studied in the field of social network analysis, whose objective is to identify a group of influential individuals to maximize the influence spread over social networks. This study aims to establish the equivalence of the two problems and develop an effective methodology for targeted immunization through the use of influence maximization. Methods We present a concise formulation of the targeted immunization problem and show its equivalence to the influence maximization problem under the framework of the Linear Threshold diffusion model. Thus the influence maximization problem, a...

Efficient Control of Epidemics Spreading on Networks: Balance between Treatment and Recovery

PLoS ONE, 2013

We analyse two models describing disease transmission and control on regular and small-world networks. We use simulations to find a control strategy that minimizes the total cost of an outbreak, thus balancing the costs of disease against that of the preventive treatment. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models.

Minimizing the social cost of an epidemic

In this paper we quantify the total cost of an epidemic spreading through a social network, accounting for both the immunization and disease costs. Previous research has typically focused on determining the optimal strategy to limit the lifetime of a disease, without considering the cost of such strategies. In the large graph limit, we calculate the exact expected disease cost for a general random graph, and we illustrate it for the specific example of an Erdos-Renyi network. We also give an upper bound on the expected disease cost for finite-size graphs. Finally, we study how to optimally perform a one-shot immunization to minimize the social cost of a disease, including both the cost of the disease and the cost of immunization.