SPATIO-TEMPORAL PATTERNS IN A CHOLERA TRANSMISSION MODEL

2015 ◽  
Vol 23 (03) ◽  
pp. 471-484 ◽  
Author(s):  
A. K. MISRA ◽  
MILAN TIWARI ◽  
ANUPAMA SHARMA

Cholera has been a public health threat for centuries. Unlike the biological characteristics, relatively less effort has been paid to comprehend the spatial dynamics of this disease. Therefore, in this paper, we have proposed a cholera epidemic model for variable population size and studied the spatial patterns in two-dimensional space. First, we have performed the equilibrium and local stability analysis of steady states obtained for temporal system. Afterwards, the local and global stability behavior of the endemic steady state in a spatially extended setting has been investigated. The numerical simulations have been done to investigate the spatial patterns. They show that dynamics of the cholera epidemic varies with time and space.

1996 ◽  
Vol 263 (1370) ◽  
pp. 625-631 ◽  

We investigate the behaviour of a spatially explicit model of the interaction between two parasitoid species and their common host. One parasitoid species is able to move between host subpopulations at a faster rate than the other parasitoid species which has a higher attack rate. Without space, the model has no equilibrium. With the addition of space, however, Comins & Hassell (1996) have shown that persistence of at least one parasitoid species is generally observed and coexistence of the two parasitoid species can be obtained over a range of parameter values. They observe that this persistence is accompanied by spatial segregation of the competing species within ‘self-organized’ spiral patterns. Here, we investigate the effects of adding various forms of temporal and spatio-temporal stochasticity to the model, and demonstrate that low-to-moderate levels of noise generally inhibit the system from forming clearly defined spirals. Despite this, there are still strong short-range correlations in species densities and this spatial heterogeneity is sufficient to allow persistence and coexistence of competitors. The addition of noise acts to increase the parameter range where the more mobile parasitoid is excluded by the other and decreases the range where the more mobile parasitoid excludes its competitor. Even if the perturbation is strong, for example, with all individuals in a randomly selected 10% of sites being eliminated at each generation, then persistence still occurs and coexistence can be achieved over a suitable range of parameters. Again, the competitive advantage of the more mobile parasitoid is reduced in the presence of this perturbation.


2013 ◽  
Vol 280 (1770) ◽  
pp. 20131174 ◽  
Author(s):  
Daihai He ◽  
Jonathan Dushoff ◽  
Raluca Eftimie ◽  
David J. D. Earn

Understanding spatial patterns of influenza transmission is important for designing control measures. We investigate spatial patterns of laboratory-confirmed influenza A across Canada from October 1999 to August 2012. A statistical analysis (generalized linear model) of the seasonal epidemics in this time period establishes a clear spatio-temporal pattern, with influenza emerging earlier in western provinces. Early emergence is also correlated with low temperature and low absolute humidity in the autumn. For the richer data from the 2009 pandemic, a mechanistic mathematical analysis, based on a transmission model, shows that both school terms and weather had important effects on pandemic influenza transmission.


2016 ◽  
Vol 24 (04) ◽  
pp. 431-456 ◽  
Author(s):  
A. K. MISRA ◽  
ALOK GUPTA

Understanding the spatio-temporal dynamics of cholera outbreaks may help in devising more effective control procedures. In this paper, we have considered a reaction–diffusion system for biological control of cholera epidemic. Firstly, we have focused on temporal evolution of cholera in a region and its control using lytic bacteriophage in the aquatic reservoirs. Then, we have explored the effect of spatial dispersion of populations on the disease dynamics. We have observed the onset of sustained oscillations via Hopf-bifurcation for the endemic state of temporal system. This onset of fluctuations in populations depends upon the phage adsorption rate. But in the spatially extended setting, all the populations stabilize i.e., the spatio-temporal distribution of all the populations becomes uniform. Some numerical computations have been done to verify analytical results.


2004 ◽  
Vol 10 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Stephan Altmeyer ◽  
Rudolf M. Füchslin ◽  
John S. McCaskill

Sequence folding is known to determine the spatial structure and catalytic function of proteins and nucleic acids. We show here that folding also plays a key role in enhancing the evolutionary stability of the intermolecular recognition necessary for the prevalent mode of catalytic action in replication, namely, in trans, one molecule catalyzing the replication of another copy, rather than itself. This points to a novel aspect of why molecular life is structured as it is, in the context of life as it could be: folding allows limited, structurally localized recognition to be strongly sensitive to global sequence changes, facilitating the evolution of cooperative interactions. RNA secondary structure folding, for example is shown to be able to stabilize the evolution of prolonged functional sequences, using only a part of this length extension for intermolecular recognition, beyond the limits of the (cooperative) error threshold. Such folding could facilitate the evolution of polymerases in spatially heterogeneous systems. This facilitation is, in fact, vital because physical limitations prevent complete sequence-dependent discrimination for any significant-size biopolymer substrate. The influence of partial sequence recognition between biopolymer catalysts and complex substrates is investigated within a stochastic, spatially resolved evolutionary model of trans catalysis. We use an analytically tractable nonlinear master equation formulation called PRESS (McCaskill et al., Biol. Chem. 382: 1343–1363), which makes use of an extrapolation of the spatial dynamics down from infinite dimensional space, and compare the results with Monte Carlo simulations.


1986 ◽  
Vol 23 (02) ◽  
pp. 283-296 ◽  
Author(s):  
Peter Donnelly

A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.


2017 ◽  
Author(s):  
Gorka Mendiguren ◽  
Julian Koch ◽  
Simon Stisen

Abstract. Distributed hydrological models are traditionally evaluated against discharge stations, emphasizing the temporal and neglecting the spatial component of a model. The present study widens the traditional paradigm by highlighting spatial patterns of evapotranspiration (ET), a key variable at the land-atmosphere interface, obtained from two different approaches at the national scale of Denmark. The first approach is based on a national water resources model (DK-model), using the MIKE-SHE model code, and the second approach utilizes a two source energy balance model (TSEB) driven mainly by satellite remote sensing data. The main hypothesis of the study is that while both approaches are essentially estimates, the spatial patterns of the remote sensing based approach are explicitly driven by observed land surface temperature and therefore represent the most direct spatial pattern information of ET; enabling its use for distributed hydrological model evaluation. Ideally the hydrological model simulation and remote sensing based approach should present similar spatial patterns and driving mechanism of ET. However, the spatial comparison showed that the differences are significant and indicating insufficient spatial pattern performance of the hydrological model. The differences in spatial patterns can partly be explained by the fact that the hydrological model is configured to run in 6 domains that are calibrated independently from each other, as it is often the case for large scale multi-basin calibrations. Furthermore, the model incorporates predefined temporal dynamics of Leaf Area Index (LAI), root depth (RD) and Crop coefficient (Kc) for each land cover type. This zonal approach of model parametrization ignores the spatio-temporal complexity of the natural system. To overcome this limitation, the study features a modified version of the DK-Model in which LAI, RD, and KC are empirically derived using remote sensing data and detailed soil property maps in order to generate a higher degree of spatio-temporal variability and spatial consistency between the 6 domains. The effects of these changes are analyzed by using the empirical orthogonal functions (EOF) analysis to evaluate spatial patterns. The EOF-analysis shows that including remote sensing derived LAI, RD and KC in the distributed hydrological model adds spatial features found in the spatial pattern of remote sensing based ET.


2021 ◽  
Vol 25 (2) ◽  
pp. 957-982 ◽  
Author(s):  
Petra Hulsman ◽  
Hubert H. G. Savenije ◽  
Markus Hrachowitz

Abstract. Satellite observations can provide valuable information for a better understanding of hydrological processes and thus serve as valuable tools for model structure development and improvement. While model calibration and evaluation have in recent years started to make increasing use of spatial, mostly remotely sensed information, model structural development largely remains to rely on discharge observations at basin outlets only. Due to the ill-posed inverse nature and the related equifinality issues in the modelling process, this frequently results in poor representations of the spatio-temporal heterogeneity of system-internal processes, in particular for large river basins. The objective of this study is thus to explore the value of remotely sensed, gridded data to improve our understanding of the processes underlying this heterogeneity and, as a consequence, their quantitative representation in models through a stepwise adaptation of model structures and parameters. For this purpose, a distributed, process-based hydrological model was developed for the study region, the poorly gauged Luangwa River basin. As a first step, this benchmark model was calibrated to discharge data only and, in a post-calibration evaluation procedure, tested for its ability to simultaneously reproduce (1) the basin-average temporal dynamics of remotely sensed evaporation and total water storage anomalies and (2) their temporally averaged spatial patterns. This allowed for the diagnosis of model structural deficiencies in reproducing these temporal dynamics and spatial patterns. Subsequently, the model structure was adapted in a stepwise procedure, testing five additional alternative process hypotheses that could potentially better describe the observed dynamics and pattern. These included, on the one hand, the addition and testing of alternative formulations of groundwater upwelling into wetlands as a function of the water storage and, on the other hand, alternative spatial discretizations of the groundwater reservoir. Similar to the benchmark, each alternative model hypothesis was, in a next step, calibrated to discharge only and tested against its ability to reproduce the observed spatio-temporal pattern in evaporation and water storage anomalies. In a final step, all models were re-calibrated to discharge, evaporation and water storage anomalies simultaneously. The results indicated that (1) the benchmark model (Model A) could reproduce the time series of observed discharge, basin-average evaporation and total water storage reasonably well. In contrast, it poorly represented time series of evaporation in wetland-dominated areas as well as the spatial pattern of evaporation and total water storage. (2) Stepwise adjustment of the model structure (Models B–F) suggested that Model F, allowing for upwelling groundwater from a distributed representation of the groundwater reservoir and (3) simultaneously calibrating the model with respect to multiple variables, i.e. discharge, evaporation and total water storage anomalies, provided the best representation of all these variables with respect to their temporal dynamics and spatial patterns, except for the basin-average temporal dynamics in the total water storage anomalies. It was shown that satellite-based evaporation and total water storage anomaly data are not only valuable for multi-criteria calibration, but can also play an important role in improving our understanding of hydrological processes through the diagnosis of model deficiencies and stepwise model structural improvement.


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