High risk landscapes of Japanese encephalitis virus outbreaks in India converge on wetlands, rainfed agriculture, wild Ardeidae, and domestic pigs

Japanese encephalitis constitutes a significant burden of disease across Asia, particularly in India, with high mortality in children. This zoonotic mosquito-borne disease is caused by the Flavivirus, Japanese encephalitis virus (JEV), and circulates in wild ardeid bird and domestic pig reservoirs both of which generate sufficiently high viremias to infect vector mosquitoes, which can then subsequently infect humans. The landscapes of these hosts, particularly in the context of anthropogenic ecotones and resulting wildlife-livestock interfaces, are poorly understood and thus significant knowledge gaps in the epidemiology and infection ecology of JEV persist, which impede optimal control and prevention of outbreaks. The current study investigated the landscape epidemiology of JEV outbreaks in India over the period 2010 to 2020 based on national human disease surveillance data. Outbreaks were modelled as an inhomogeneous Poisson point process. Outbreak risk was strongly associated with the habitat suitability of ardeid birds and pig density, and shared landscapes between fragmented rainfed agriculture and both river and freshwater marsh wetlands. Moreover, risk scaled with Ardeidae habitat suitability, but was consistent across scale with respect to pig density and rainfed agriculture-wetland mosaics. The results from this work provide a more complete understanding of the landscape epidemiology and infection ecology of JEV in India and suggest important priorities for control and prevention across fragmented terrain comprised of wildlife-livestock interface that favours spillover to humans.

A numerical method for computing interval distributions for an inhomogeneous Poisson point process modified by random dead times

The inhomogeneous Poisson point process is a common model for time series of discrete, stochastic events. When an event from a point process is detected, it may trigger a random dead time in the detector, during which subsequent events will fail to be detected. It can be difficult or impossible to obtain a closed-form expression for the distribution of intervals between detections, even when the rate function (often referred to as the intensity function) and the dead-time distribution are given. Here, a method is presented to numerically compute the interval distribution expected for any arbitrary inhomogeneous Poisson point process modified by dead times drawn from any arbitrary distribution. In neuroscience, such a point process is used to model trains of neuronal spikes triggered by the detection of excitatory events while the neuron is not refractory. The assumptions of the method are that the process is observed over a finite observation window and that the detector is not in a dead state at the start of the observation window. Simulations are used to verify the method for several example point processes. The method should be useful for modeling and understanding the relationships between the rate functions and interval distributions of the event and detection processes, and how these relationships depend on the dead-time distribution.

A ‘How-to’ Guide for Interpreting Parameters in Resource- and Step-Selection Analyses

Resource-selection and step-selection analyses allow researchers to link animals to their environment and are commonly used to address questions related to wildlife management and conservation efforts. Step-selection analyses that incorporate movement characteristics, referred to as integrated step-selection analyses, are particularly appealing because they allow modeling of both movement and habitat-selection processes.Despite their popularity, many users struggle with interpreting parameters in resource-selection and step-selection functions. Integrated step-selection analyses also require several additional steps to translate model parameters into a full-fledged movement model, and the mathematics supporting this approach can be challenging for biologists to understand.Using simple examples, we demonstrate how weighted distribution theory and the inhomogeneous Poisson point-process model can facilitate parameter interpretation in resource-selection and step-selection analyses. Further, we provide a “how to” guide illustrating the steps required to implement integrated step-selection analyses using the amt package.By providing clear examples with open-source code, we hope to make resource-selection and integrated step-selection analyses more understandable and accessible to end users.

Randomly Weighted $d$-Complexes: Minimal Spanning Acycles and Persistence Diagrams

A weighted $d$-complex is a simplicial complex of dimension $d$ in which each face is assigned a real-valued weight. We derive three key results here concerning persistence diagrams and minimal spanning acycles (MSAs) of such complexes. First, we establish an equivalence between the MSA face-weights and death times in the persistence diagram. Next, we show a novel stability result for the MSA face-weights which, due to our first result, also holds true for the death and birth times, separately. Our final result concerns a perturbation of a mean-field model of randomly weighted $d$-complexes. The $d$-face weights here are perturbations of some i.i.d. distribution while all the lower-dimensional faces have a weight of $0$. If the perturbations decay sufficiently quickly, we show that suitably scaled extremal nearest face-weights, face-weights of the $d$-MSA, and the associated death times converge to an inhomogeneous Poisson point process. This result completely characterizes the extremal points of persistence diagrams and MSAs. The point process convergence and the asymptotic equivalence of three point processes are new for any weighted random complex model, including even the non-perturbed case. Lastly, as a consequence of our stability result, we show that Frieze's $\zeta(3)$ limit for random minimal spanning trees and the recent extension to random MSAs by Hino and Kanazawa also hold in suitable noisy settings.

Testing hypotheses on population dynamics: A test for the inhomogeneous Poisson point process model

In this paper, a test for hypotheses on population dynamics is presented alongside an implementation of said test for R. The test is based on the assumption that the sample, consisting of points on a time axis, is a realization of a Poisson point process (PPP). There are no restrictions on the shapes of the rate functions that are regulating the PPP, type 2 errors can be calculated and the test is optimal in the sense that it is a uniform most powerful (UMP) test. So for every significance level a, the presented test has a lower type 2 error than every other test having the same significance level a. The test is applicable to all models based on PPPs, including models in spatial dimensions. It can be generalized and expanded in different ways, such as testing larger hypotheses, incorporating prior knowledge, and constructing confidence regions that can be used to obtain upper or lower bounds on rate functions.

Analytical Expressions for Formal Kinetics

In recent papers Rios and Villa resorted to developments in stochastic geometry to revisit theclassical KJMA theory and generalize it for situations in which nuclei were located in space accordingto both homogeneous and inhomogeneous Poisson point processes as well as according to Materncluster process and surface and bulk nucleation in small specimens. Rigorous mathematical methodswere employed to ensure the reliability of the new expressions. These results are briefly described.Analytical expression for inhomogeneous Poisson point process nucleation gives very good agreementwith Cellular Automata simulations. Cellular Automata simulations complement the analyticalsolutions by showing the corresponding microstructural evolution. These new results considerablyexpand the range of situations for which analytical solutions are available.

Approximate decomposition of some modulated-Poisson Voronoi tessellations

We consider the Voronoi tessellation of Euclidean space that is generated by an inhomogeneous Poisson point process whose intensity takes different constant values on sets of some finite partition of the space. Considering the Voronoi cells as marks associated with points of the point process, we prove that the intensity measure (mean measure) of the marked Poisson point process admits an approximate decomposition formula. The true value is approximated by a mixture of respective intensity measures for homogeneous models, while the explicit upper bound for the remainder term can be computed numerically for a large class of practical examples. By the Campbell formula, analogous approximate decompositions are deduced for the Palm distributions of individual cells. This approach makes possible the analysis of a wide class of inhomogeneous-Poisson Voronoi tessellations, by means of formulae and estimates already established for homogeneous cases. Our analysis applies also to the Poisson process modulated by an independent stationary random partition, in which case the error of the approximation of the double-stochastic-Poisson Voronoi tessellation depends on some integrated linear contact distribution functions of the boundaries of the partition elements.