Percolation and Epidemic Thresholds in Clustered Networks

We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks extending, thus, this result to a wide variety of real scale-free networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.Comment: 4 Pages and 3 Figures. Final version to appear in PR

Emergent spatial correlations in stochastically evolving populations

We study the spatial pattern formation and emerging long range correlations in a model of three species coevolving in space and time according to stochastic contact rules. Analytical results for the pair correlation functions, based on a truncation approximation and supported by computer simulations, reveal emergent strategies of survival for minority agents based on selection of patterns. Minority agents exhibit defensive clustering and cooperative behavior close to phase transitions.Comment: 11 pages, 4 figures, Adobe PDF forma

Coupled Contagion Dynamics of Fear and Disease: Mathematical and Computational Explorations

Background: In classical mathematical epidemiology, individuals do not adapt their contact behavior during epidemics. They do not endogenously engage, for example, in social distancing based on fear. Yet, adaptive behavior is welldocumented in true epidemics. We explore the effect of including such behavior in models of epidemic dynamics. Methodology/Principal Findings: Using both nonlinear dynamical systems and agent-based computation, we model two interacting contagion processes: one of disease and one of fear of the disease. Individuals can ‘‘contract’ ’ fear through contact with individuals who are infected with the disease (the sick), infected with fear only (the scared), and infected with both fear and disease (the sick and scared). Scared individuals–whether sick or not–may remove themselves from circulation with some probability, which affects the contact dynamic, and thus the disease epidemic proper. If we allow individuals to recover from fear and return to circulation, the coupled dynamics become quite rich, and can include multiple waves of infection. We also study flight as a behavioral response. Conclusions/Significance: In a spatially extended setting, even relatively small levels of fear-inspired flight can have a dramatic impact on spatio-temporal epidemic dynamics. Self-isolation and spatial flight are only two of many possible actions that fear-infected individuals may take. Our main point is that behavioral adaptation of some sort must b

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider

Systems medicine and infection

By using a systems based approach, mathematical and computational techniques can be used to develop models that describe the important mechanisms involved in infectious diseases. An iterative approach to model development allows new discoveries to continually improve the model, and ultimately increase the accuracy of predictions. SIR models are used to describe epi demics, predicting the extent and spread of disease. Genome-wide genotyping and sequencing technologies can be used to identify the biological mechanisms behind diseases. These tools help to build strategies for disease prevention and treatment, an example being the recent outbreak of Ebola in West Africa where these techniques were deployed. HIV is a complex disease where much is still to be learnt about the virus and the best effective treatment. With basic mathematical modelling techniques, significant discoveries have been made over the last 20 years. With recent technological advances, the computation al resources now available and interdisciplinary cooperation, further breakthroughs are inevitable. In TB, modelling has traditionally been empirical in nature, with clinical data providing the fuel for this top-down approach. Recently, projects have begun to use data derived from laboratory experiments and clinical trials to create mathematical models that describe the mechanisms responsible for the disease. A systems medicine approach to infection modelling helps identify important biological questions that then direct future experiments , the results of which improve the model in an iterative cycle . This means that data from several model systems can be integrated and synthesised to explore complex biological systems .Postprin

Epidemiological impact of waning immunization on a vaccinated population

This is an epidemiological SIRV model based study that is de- signed to analyze the impact of vaccination in containing infection spread, in a 4-tiered population compartment comprised of susceptible, infected, recov- ered and vaccinated agents. While many models assume a lifelong protection through vaccination, we focus on the impact of waning immunization due to conversion of vaccinated and recovered agents back to susceptible ones. Two asymptotic states exist, the \disease-free equilibrium" and the \endemic equi- librium" and we express the transitions between these states as function of the vaccination and conversion rates and using the basic reproduction number. We nd that the vaccination of newborns and adults have dierent consequences on controlling an epidemic. Also, a decaying disease protection within the re- covered sub-population is not sucient to trigger an epidemic on the linear level. We perform simulations for a parameter set modelling a disease with waning immunization like pertussis. For a diusively coupled population, a transition to the endemic state can proceed via the propagation of a traveling infection wave, described successfully within a Fisher-Kolmogorov framework

Exact equations for SIR epidemics on tree graphs

We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected. We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph. Moreover, this “deterministic” representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically