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      Spatial Patterns of Spread of Dengue with Human and Vector Mobility

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          Abstract

          Dengue is a vector borne disease transmitted to humans by {\it{Aedes Aegypti}} mosquitoes carrying Dengue virus of different serotypes. Primarily an urban epidemic, Dengue exhibits complex spatial and temporal dynamics, influenced by many biological, human and environmental factors. However, most of the existing models neglect the spatial factors influencing the spread of Dengue. This work sheds light on how Dengue parameters and human mobility changes the spatial spread of the infection and size of the epidemic. We model the Dengue as a stochastic Cellular Automata (CA) process following Susceptible, Exposed, Infected, Recovered (SEIR) -Susceptible, Exposed, Infected (SEI)- for human and vector dynamics respectively in each cell, and analyze the spatial and temporal spreading disease using parameters from field studies. We use the data on mosquito density from Ahmedabad city of India as input to our model to predict the dynamics of Dengue incidence and compare it to the reported data on the prevalence of the disease from 2006-2012. We find that for certain infection rates, CA model closely reproduces observed peaks and intensity. We used data based statistical models of human mobility such as exponential step length and super diffusive L\'evy flight to study mobility effects on Dengue spreading within the city. We find an interesting result that inclusion of human mobility in many cases can decrease the incidence of Dengue, and may suppress the infection completely. The scale and intensity of reduction depend on the relative strengths of infection transmission rate and mobility step length. The primarily reason for decline can be attributed to the significant fraction of the susceptible and exposed population moving to the regions where majority have already recovered and can no longer be infected.

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          Understanding individual human mobility patterns

          Despite their importance for urban planning, traffic forecasting, and the spread of biological and mobile viruses, our understanding of the basic laws governing human motion remains limited thanks to the lack of tools to monitor the time resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six month period. We find that in contrast with the random trajectories predicted by the prevailing Levy flight and random walk models, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time independent characteristic length scale and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent based modeling.
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            The scaling laws of human travel

            The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronise populations of interacting species, stabilise them, and diversify gene pools [1-3]. Human travelling, e.g. is responsible for the geographical spread of human infectious disease [4-9]. In the light of increasing international trade, intensified human mobility and an imminent influenza A epidemic [10] the knowledge of dynamical and statistical properties of human travel is thus of fundamental importance. Despite its crucial role, a quantitative assessment of these properties on geographical scales remains elusive and the assumption that humans disperse diffusively still prevails in models. Here we report on a solid and quantitative assessment of human travelling statistics by analysing the circulation of bank notes in the United States. Based on a comprehensive dataset of over a million individual displacements we find that dispersal is anomalous in two ways. First, the distribution of travelling distances decays as a power law, indicating that trajectories of bank notes are reminiscent of scale free random walks known as Levy flights. Secondly, the probability of remaining in a small, spatially confined region for a time T is dominated by algebraically long tails which attenuate the superdiffusive spread. We show that human travelling behaviour can be described mathematically on many spatiotemporal scales by a two parameter continuous time random walk model to a surprising accuracy and conclude that human travel on geographical scales is an ambivalent effectively superdiffusive process.
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              Climate variability and change in the United States: potential impacts on vector- and rodent-borne diseases.

              Diseases such as plague, typhus, malaria, yellow fever, and dengue fever, transmitted between humans by blood-feeding arthropods, were once common in the United States. Many of these diseases are no longer present, mainly because of changes in land use, agricultural methods, residential patterns, human behavior, and vector control. However, diseases that may be transmitted to humans from wild birds or mammals (zoonoses) continue to circulate in nature in many parts of the country. Most vector-borne diseases exhibit a distinct seasonal pattern, which clearly suggests that they are weather sensitive. Rainfall, temperature, and other weather variables affect in many ways both the vectors and the pathogens they transmit. For example, high temperatures can increase or reduce survival rate, depending on the vector, its behavior, ecology, and many other factors. Thus, the probability of transmission may or may not be increased by higher temperatures. The tremendous growth in international travel increases the risk of importation of vector-borne diseases, some of which can be transmitted locally under suitable circumstances at the right time of the year. But demographic and sociologic factors also play a critical role in determining disease incidence, and it is unlikely that these diseases will cause major epidemics in the United States if the public health infrastructure is maintained and improved.
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                Author and article information

                Journal
                1409.0965

                Evolutionary Biology
                Evolutionary Biology

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