Equation-Free Multiscale Computational Analysis of Individual-Based Epidemic Dynamics on Networks

The surveillance, analysis and ultimately the efficient long-term prediction and control of epidemic dynamics appear to be one of the major challenges nowadays. Detailed atomistic mathematical models play an important role towards this aim. In this work it is shown how one can exploit the Equation Free approach and optimization methods such as Simulated Annealing to bridge detailed individual-based epidemic simulation with coarse-grained, systems-level, analysis. The methodology provides a systematic approach for analyzing the parametric behavior of complex/ multi-scale epidemic simulators much more efficiently than simply simulating forward in time. It is shown how steady state and (if required) time-dependent computations, stability computations, as well as continuation and numerical bifurcation analysis can be performed in a straightforward manner. The approach is illustrated through a simple individual-based epidemic model deploying on a random regular connected graph. Using the individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of Simulated Annealing I compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level under a pairwise representation perspective

Maternally derived microduplications at 15q11-q13: implication of imprinted genes in psychotic illness

Contains fulltext : 97099.pdf (publisher's version ) (Closed access)OBJECTIVE: Rare copy number variants have been implicated in different neurodevelopmental disorders, with the same copy number variants often increasing risk of more than one of these phenotypes. In a discovery sample of 22 schizophrenia patients with an early onset of illness (10-15 years of age), the authors observed in one patient a maternally derived 15q11-q13 duplication overlapping the Prader-Willi/Angelman syndrome critical region. This prompted investigation of the role of 15q11-q13 duplications in psychotic illness. METHOD: The authors scanned 7,582 patients with schizophrenia or schizoaffective disorder and 41,370 comparison subjects without known psychiatric illness for copy number variants at 15q11-q13 and determined the parental origin of duplications using methylation-sensitive Southern hybridization analysis. RESULTS: Duplications were found in four case patients and five comparison subjects. All four case patients had maternally derived duplications (0.05%), while only three of the five comparison duplications were maternally derived (0.007%), resulting in a significant excess of maternally derived duplications in case patients (odds ratio=7.3). This excess is compatible with earlier observations that risk for psychosis in people with Prader-Willi syndrome caused by maternal uniparental disomy is much higher than in those caused by deletion of the paternal chromosome. CONCLUSIONS: These findings suggest that the presence of two maternal copies of a fragment of chromosome 15q11.2-q13.1 that overlaps with the Prader-Willi/Angelman syndrome critical region may be a rare risk factor for schizophrenia and other psychoses. Given that maternal duplications of this region are among the most consistent cytogenetic observations in autism, the findings provide further support for a shared genetic etiology between autism and psychosis