Optimal Control of Epidemics in the Presence of Heterogeneity

We seek to identify and address how different types of heterogeneity affect the optimal control of epidemic processes in social, biological, and computer networks. Epidemic processes encompass a variety of models of propagation that are based on contact between agents. Assumptions of homogeneity of communication rates, resources, and epidemics themselves in prior literature gloss over the heterogeneities inherent to such networks and lead to the design of sub-optimal control policies. However, the added complexity that comes with a more nuanced view of such networks complicates the generalizing of most prior work and necessitates the use of new analytical methods. We first create a taxonomy of heterogeneity in the spread of epidemics. We then model the evolution of heterogeneous epidemics in the realms of biology and sociology, as well as those arising from practice in the fields of communication networks (e.g., DTN message routing) and security (e.g., malware spread and patching). In each case, we obtain computational frameworks using Pontryagin’s Maximum Principle that will lead to the derivation of dynamic controls that optimize general, context-specific objectives. We then prove structures for each of these vectors of optimal controls that can simplify the derivation, storage, and implementation of optimal policies. Finally, using simulations and real-world traces, we examine the benefits achieved by including heterogeneity in the control decision, as well as the sensitivity of the models and the controls to model parameters in each case

Efficient dynamic centrality metrics for election advertising - a case study

In prior work [1], we have shown how advertising channels should be chosen by a budget-constrained electoral campaign. In this poster, we apply the resulting proposed algorithm to the MIT Social Evolution [2] data-set (N=84), which captured political discussions, inclinations, and voting behaviors around the 2008 US Presidential Election within a student dorm. We compare the resulting centrality metrics developed from our algorithm (which have a direct mapping to optimal channel choice decisions) against more traditional static centralities, and show how employing them leads to more votes. [1] Eshghi, S., Preciado, V.M., Sarkar, S., Venkatesh, S.S., Zhao, Q., D\u27Souza, R. and Swami, A., 2017. Spread, then Target, and Advertise in Waves: Optimal Capital Allocation Across Advertising Channels. arXiv preprint arXiv:1702.03432. [2] A. Madan, M. Cebrian, S. Moturu, K. Farrahi, A. Pentland, Sensing the \u27Health State\u27 of a Community, Pervasive Computing, Vol. 11, No. 4, pp. 36-45 Oct 201

A computational framework for modelling inter-group behaviour using psychological theory

Psychological theories of inter-group behaviour offer justified representations for interaction, influence, and motivation for coalescence. Agent-based modelling of this behaviour, using evolutionary approaches, further provides a powerful tool to examine the implications of these theories in a dynamic context. In particular, this can enhance our understanding of the escalation of hostility and warfare, and its mitigation, contributing to policy and interventions. In this paper we propose a framework through which social psychology can be embedded in computation for the examination of inter-group behaviour. We examine how various social-psychological theories can be embedded in evolutionary models, and identify ways in which visualisation can support the objective assessment of emergent behaviour. We also discuss how real-world data can be used to parameterise scenarios on which modelling is conducted

Mathematical models for social group behavior

In this paper, we seek to identity how mathematical and economic analysis can be used to gain insights about the mutation of social groups. Group mutability has been studied in multiple domains, with insights generated on significant factors at differing scales. Mathematical modeling enables the simultaneous study of such phenomena, understanding interactions and generating hypotheses for experiments. In particular, we focus on group fracture, where individuals leave groups of which they are members. For example, this can be due to perceived differences with other group members due to norm related conflict (such as extreme actions by some members). Our aim is to consider simple mathematical models incorporating a selection of social and psychological theory which describes these phenomena as a way to understand their interplay, and describe the trade-offs and challenges. This will help a federation model the behavior of extremist groups, and determine not only when an intervention is necessary, but also the best course of action to take to induce the fracture of such groups. This paper is an exploratory investigation into methods of achieving this goal and evaluating the usefulness of the outputs to federations

Stability and fracture of social groups

In this paper, we present a mathematical model for the mutation of social groups. Group mutability has been studied in multiple domains, with insights generated on significant factors at differing scales. Mathematical modeling enables the simultaneous study of such phenomena, understanding interactions and generating hypotheses for experiments. In particular, we focus on group fracture, where individuals leave groups of which they are members. For example, this can be due to perceived differences with other group members due to norm related conflict (such as extreme actions by some members). Our aim is to consider simple mathematical models incorporating a selection of social and psychological theory which describes these phenomena as a way to understand their interplay, and describe the trade-offs and challenges