Search

We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic effects dominate and show that epidemics tend to happen faster than deterministic calculations predict. If an outbreak is sufficiently large, stochastic effects are negligible and we modify the standard ordinary differential equation (ODE) model to accommodate age-of-infection effects. We avoid the use of partial differential equations which typically appear in related models. We introduce a "memoryless" ODE system which approximates the true solutions. Finally, we analyze the transition from the stochastic to the deterministic phase.

When an infectious disease strikes a population, the number of newly reported cases is often the only available information that one can obtain during early stages of the outbreak. An important goal of early outbreak analysis is to obtain a reliable estimate for the basic reproduction number, $R_{0}$, from the limited information available. We present a novel method that enables us to make a reliable real-time estimate of the reproduction number at a much earlier stage compared to other available methods. Our method takes into account the possibility that a disease has a wide distribution of infectious period and that the degree distribution of the contact network is heterogeneous. We validate our analytical framework with numerical simulations., Comment: 29 pages, 13 Figures

Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes -- in which final state can be obtained by studying the underlying network percolation properties -- have raised formidable interest. In this paper, we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability. As previously demonstrated, the multitype approach allows many non-trivial mixing patterns such as assortativity and clustering between nodes. We derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion. We also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism. We further show that the multitype approach, by naturally allowing heterogeneity in the bond occupation probability, overcomes some of the correlation issues encountered by previous models. We illustrate this point in the context of contact network epidemiology., Comment: 10 pages, 5 figures. Minor modifications were made in figures 3, 4 and 5 and in the text. Explanations and references were added

Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the expense of simplifying the pattern of transmission. The second approach uses network theory to incorporate detailed information pertaining to the underlying contact structure among individuals while disregarding the progression of time during outbreaks. So far, the only alternative that enables the integration of both aspects of disease propagation simultaneously while preserving the variety of outcomes has been to abandon the analytical approach and rely on computer simulations. We offer a new analytical framework, which incorporates both the complexity of contact network structure and the time progression of disease spread. Furthermore, we demonstrate that this framework is equally effective on finite- and "infinite"-size networks. This formalism can be equally applied to similar percolation phenomena on networks in other areas of science and technology., Comment: 17 pages, 7 figures. This version (v4) has been accepted by Physical Review E on December 9, 2008. The first version (v1) of this paper supersedes arXiv:0710.3420 . Version v2, v3 and v4 consist of the first (discrete time) part of v1. It contains a new section IV for comparison with different models. The continuous time part of v1 will appear as a separate contribution

Two crucial elements facilitate the understanding and control of communicable disease spread within a social setting. These components are, the underlying contact structure among individuals that determines the pattern of disease transmission; and the evolution of this pattern over time. Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches to incorporate these elements. The first approach, generally known as compartmental modeling, addresses the time evolution of disease spread at the expense of simplifying the pattern of transmission. On the other hand, the second approach uses network theory to incorporate detailed information pertaining to the underlying contact structure among individuals. However, while providing accurate estimates on the final size of outbreaks/epidemics, this approach, in its current formalism, disregards the progression of time during outbreaks. So far, the only alternative that enables the integration of both aspects of disease spread simultaneously has been to abandon the analytical approach and rely on computer simulations. We offer a new analytical framework based on percolation theory, which incorporates both the complexity of contact network structure and the time progression of disease spread. Furthermore, we demonstrate that this framework is equally effective on finite- and "infinite"-size networks. Application of this formalism is not limited to disease spread; it can be equally applied to similar percolation phenomena on networks in other areas in science and technology., Comment: 20 pages, 6 figures

The threat of avian influenza and the 2004-2005 influenza vaccine supply shortage in the United States has sparked a debate about optimal vaccination strategies to reduce the burden of morbidity and mortality caused by the influenza virus. We present a comparative analysis of two classes of suggested vaccination strategies: mortality-based strategies that target high risk populations and morbidity-based that target high prevalence populations. Applying the methods of contact network epidemiology to a model of disease transmission in a large urban population, we evaluate the efficacy of these strategies across a wide range of viral transmission rates and for two different age-specific mortality distributions. We find that the optimal strategy depends critically on the viral transmission level (reproductive rate) of the virus: morbidity-based strategies outperform mortality-based strategies for moderately transmissible strains, while the reverse is true for highly transmissible strains. These results hold for a range of mortality rates reported for prior influenza epidemics and pandemics. Furthermore, we show that vaccination delays and multiple introductions of disease into the community have a more detrimental impact on morbidity-based strategies than mortality-based strategies. If public health officials have reasonable estimates of the viral transmission rate and the frequency of new introductions into the community prior to an outbreak, then these methods can guide the design of optimal vaccination priorities. When such information is unreliable or not available, as is often the case, this study recommends mortality-based vaccination priorities.