Dynamics of dengue disease with human and vector mobility.

Dengue is a vector borne disease transmitted to humans by Aedes aegypti mosquitoes carrying virus of different serotypes. Dengue exhibits complex spatial and temporal dynamics, influenced by various biological, human and environmental factors. In this work, we study the dengue spread for a single serotype (DENV-1) including statistical models of human mobility with exponential step length distribution, by using reaction-diffusion equations and Stochastic Cellular Automata (SCA) approach. We analyze the spatial and temporal spreading of the disease using parameters from field studies. We choose mosquito density data from Ahmedabad city as a proxy for climate data in our SCA model. We find an interesting result that although human mobility makes the infection spread faster, there is an apparent early suppression of the epidemic compared to immobile humans. The disease extinction time is lesser when human mobility is included.

Estimation of reproduction number and non stationary spectral analysis of dengue epidemic.

In this work we analyze the post monsoon Dengue outbreaks by analyzing the transient and long term dynamics of Dengue incidences and its environmental correlates in Ahmedabad city in western India from 2005 to 2012. We calculate the reproduction number Rp using the growth rate of post monsoon Dengue outbreaks and biological parameters like host and vector incubation periods and vector mortality rate, and its uncertainties are estimated through Monte-Carlo simulations by sampling parameters from their respective probability distributions. Reduction in Female Aedes mosquito density required for an effective prevention of Dengue outbreaks is also calculated. The non stationary pattern of Dengue incidences and its climatic correlates like rainfall temperature is analyzed through Wavelet based methods. We find that the mean time lag between peak of monsoon and Dengue is 9 weeks. Monsoon and Dengue cases are phase locked from 2008 to 2012 in the 16 to maintain consistency make it "16 to 32" 32 weeks band. The duration of post monsoon outbreak has been increasing every year, especially post 2008, even though the intensity and duration of monsoon has been decreasing. Temperature and Dengue incidences show correlations in the same band, but phase lock is not stationary.

Epidemic spreading on preferred degree adaptive networks.

We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree κ. Using very simple rules for forming such preferred degree networks, we find some unusual statistical properties not found in familiar Erdös-Rényi or scale free networks. By letting κ depend on the fraction of infected individuals, we model the behavioral changes in response to how the extent of the epidemic is perceived. In our models, the behavioral adaptations can be either 'blind' or 'selective'--depending on whether a node adapts by cutting or adding links to randomly chosen partners or selectively, based on the state of the partner. For a frozen preferred network, we find that the infection threshold follows the heterogeneous mean field result λ(c)/µ = <κ>/<κ2> and the phase diagram matches the predictions of the annealed adjacency matrix (AAM) approach. With 'blind' adaptations, although the epidemic threshold remains unchanged, the infection level is substantially affected, depending on the details of the adaptation. The 'selective' adaptive SIS models are most interesting. Both the threshold and the level of infection changes, controlled not only by how the adaptations are implemented but also how often the nodes cut/add links (compared to the time scales of the epidemic spreading). A simple mean field theory is presented for the selective adaptations which capture the qualitative and some of the quantitative features of the infection phase diagram.

Testing the topological nature of the fractional quantum Hall edge.

We carry out numerical diagonalization for much larger systems than before by restricting the fractional quantum Hall (FQH) edge excitations to a basis that is exact for a short-range interaction and very accurate for the Coulomb interaction. This enables us to perform substantial tests of the predicted universality of the edge physics. Our results suggest the possibility that the behavior of the FQH edge is intrinsically nonuniversal, even in the absence of edge reconstruction, and therefore may not bear a sharp and unique relation to the nature of the bulk FQH state.