Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. Here we explore the use of dynamic bipartite graphs to model the physical contact patterns that result from movements of individuals between specific locations. The graphs are generated by large-scale individual-based urban traffic simulations built on actual census, land-use and population-mobility data. We find that the contact network among people is a strongly connected small-world-like graph with a well-defined scale for the degree distribution. However, the locations graph is scale-free, which allows highly efficient outbreak detection by placing sensors in the hubs of the locations network. Within this large-scale simulation framework, we then analyse the relative merits of several proposed mitigation strategies for smallpox spread. Our results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.

A switch in specificity of avian influenza A viruses' hemagglutinin (HA) from avian-like (alpha2-3 sialylated glycans) to human-like (alpha2-6 sialylated glycans) receptors is believed to be associated with their adaptation to infect humans. We show that a characteristic structural topology--and not the alpha2-6 linkage itself--enables specific binding of HA to alpha2-6 sialylated glycans and that recognition of this topology may be critical for adaptation of HA to bind glycans in the upper respiratory tract of humans. An integrated biochemical, analytical and data mining approach demonstrates that HAs from the human-adapted H1N1 and H3N2 viruses, but not H5N1 (bird flu) viruses, specifically bind to long alpha2-6 sialylated glycans with this topology. This could explain why H5N1 viruses have not yet gained a foothold in the human population. Our findings will enable the development of additional strategies for effective surveillance and potential therapeutic interventions for H5N1 and possibly other influenza A viruses.

Abstract3G networks are currently overloaded, due to the increasing popularity of various applications for smartphones. Offloading mobile data traffic through opportunistic communications is a promising solution to partially solve this problem, because there is almost no monetary cost for it. We propose to exploit opportunistic communications to facilitate information dissemination in the emerging Mobile Social Networks (MoSoNets) and thus reduce the amount of mobile data traffic. As a case study, we investigate the target-set selection problem for information delivery. In particular, we study how to select the target set with only k users, such that we can minimize the mobile data traffic over cellular networks. We propose three algorithms, called Greedy, Heuristic, and Random, for this problem and evaluate their performance through an extensive trace-driven simulation study. Our simulation results verify the efficiency of these algorithms for both synthetic and real-world mobility traces. For example, the Heuristic algorithm can offload mobile data traffic by up to 73.66% for a real-world mobility trace. Moreover, to investigate the feasibility of opportunistic communications for mobile phones, we implement a proof-of-concept prototype, called Opp-Off, on Nokia N900 smartphones, which utilizes their Bluetooth interface for device/service discovery and content transfer.

We develop a new randomized rounding approach for fractional vectors defined on the edge-sets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include: -low congestion multi-path routing; -richer random-graph models for graphs with a given degree-sequence; -improved approximation algorithms for: (i) throughput-maximization in broadcast scheduling, (ii) delay-minimization in broadcast scheduling, as well as (iii) capacitated vertex cover; and -fair scheduling of jobs on unrelated parallel machines.By the induction hypothesis, Pr [S 1 ∪ S 2 ∪ {x}] ≤ Pr [S 1 ∪ {x}]Pr [S 2 ] and hence (6) follows. An identical argument holds for the case where p 1 , q 1 ∈ S 2 .Case 3. p 1 ∈ S 1 and q 1 ∈ E \ (S 1 ∪ S 2 ). Let S 1 = S 1 \ {p 1 }. Exactly one of two events happens during the iteration.Event A. p 1 gets rounded to zero. In this case,By the induction hypothesis, Pr [S 1 ∪ S 2 ] ≤ Pr [S 1 ]Pr [S 2 ] and hence (6) follows. Event B. p 1 does not get rounded to zero. In this case, Pr[S 1 | T ] = Pr [S 1 ∪ {x}] Pr[S 2 | T ] = Pr [S 2 ] Pr[S 1 ∪ S 2 | T ] = Pr [S 1 ∪ S 2 ∪ {x}]. By the induction hypothesis, Pr [S 1 ∪ S 2 ∪ {x}] ≤ Pr [S 1 ∪ {x}]Pr [S 2 ] and hence (6) follows. Case 4. { p 1 , q 1 } ⊆ E \(S 1 ∪ S 2 ). In this case, Pr[S 1 | T ] = Pr [S 1 ], Pr[S 2 | T ] = Pr [S 2 ] and Pr[S 1 ∪ S 2 | T ] = Pr [S 1 ∪ S 2 ]; we are done by the induction hypothesis. This completes the proof of Theorem 2.4.

The human adaptation of influenza A viruses is critically governed by the binding specificity of the viral surface hemagglutinin (HA) to long (chain length) ␣2-6 sialylated glycan (␣2-6) receptors on the human upper respiratory tissues. A recent study demonstrated that whereas the 1918 H1N1 pandemic virus, A/South Carolina/1/1918 (SC18), with ␣2-6 binding preference transmitted efficiently, a single amino acid mutation on HA resulted in a mixed ␣2-3 sialylated glycan (␣2-3)/␣2-6 binding virus (NY18) that transmitted inefficiently. To define the biochemical basis for the observed differences in virus transmission, in this study, we have developed an approach to quantify the multivalent HA-glycan interactions. Analysis of the molecular HA-glycan contacts showed subtle changes resulting from the single amino acid variations between SC18 and NY18. The effect of these changes on glycan binding is amplified by multivalency, resulting in quantitative differences in their long ␣2-6 glycan binding affinities. Furthermore, these differences are also reflected in the markedly distinct binding pattern of SC18 and NY18 HA to the physiological glycans present in human upper respiratory tissues. Thus, the dramatic lower binding affinity of NY18 to long ␣2-6 glycans, as against a mixed ␣2-3/6 binding, correlates with its inefficient transmission. In summary, this study establishes a quantitative biochemical correlate for influenza A virus transmission.hemagglutinin ͉ multivalency ͉ sialylated glycans T he Spanish influenza pandemic of 1918 caused by the H1N1 subtype virus resulted in Ϸ20 million to 50 million deaths worldwide (1). The emergence of avian influenza H5N1 viruses that are able to infect humans (Ͼ300 known cases) and produce a high mortality rate (Ϸ200 deaths) has raised serious global health concerns. Significantly, adaptation of these viruses for efficient human-human transmission could result in a new influenza pandemic, a public health disaster of tragic proportions.The critical step in the host infection of influenza viruses is the binding of their viral surface hemagglutinin (HA) to sialylated glycan receptors on the epithelial cell surface of the host organism (2-6). The evolution of pandemic viruses involves crossing-over of avian influenza viruses (natural host) to humans and adaptation to the human host for subsequent infection and human-human transmission (2, 7). This cross-over is believed to involve mutations in HA that switch its glycan receptor preference from ␣2-3 sialylated (␣2-3) to ␣2-6 sialylated (␣2-6) glycans found in abundance in human upper respiratory epithelia (3)(4)(5) 8). The human upper respiratory tract ␣2-6 receptor adaptation of HA is a critical step in permitting the viruses to infect and efficiently replicate in these tissues, leading to rapid humanhuman transmission (8). Several studies have been performed to elucidate the distribution of glycans in human upper respiratory tissues (4,(8)(9)(10). We recently demonstrated that human upper airways express a diversity of ␣2-6 structur...