scholarly journals Studying and approximating spatio–temporal models for epidemic spread and control

1998 ◽  
Vol 353 (1378) ◽  
pp. 2153-2162 ◽  
Author(s):  
J. A. N. Filipe ◽  
G. J. Gibson
Keyword(s):  
Control Strategies ◽  
Secondary Infection ◽  
Contact Process ◽  
Approximate Solutions ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Range Interaction ◽  
Temporal Models ◽  
Spatio Temporal ◽  
And Control

A class of simple spatio–temporal stochastic models for the spread and control of plant disease is investigated. We consider a lattice–based susceptible–infected model in which the infection of a host occurs through two distinct processes: a background infective challenge representing primary infection from external sources, and a short–range interaction representing the secondary infection of susceptibles by infectives within the population. Recent data–modelling studies have suggested that the above model may describe the spread of aphid–borne virus diseases in orchards. In addition, we extend the model to represent the effects of different control strategies involving replantation (or recovery). The Contact Process is a particular case of this model. The behaviour of the model has been studied using Cellular–Automata simulations. An alternative approach is to formulate a set of deterministic differential equations that captures the essential dynamics of the stochastic system. Approximate solutions to this set of equations, describing the time evolution over the whole parameter range, have been obtained using the pairwise approximation (PA) as well as the most commonly used mean–field approximation (MF). Comparison with simulation results shows that PA is significantly superior to MF, predicting accurately both transient and long–run, stationary behaviour over relevant parts of the parameter space. The conditions for the validity of the approximations to the present model and extensions thereof are discussed.

Approximate Solutions

2020 ◽  
pp. 106-158
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Random Walk ◽  
Mean Field ◽  
Gaussian Model ◽  
Spherical Model ◽  
Approximate Solutions ◽  
Field Approximation ◽  
Approximation Schemes ◽  
Mean Field Approximation ◽  
Exactly Solvable ◽  
The Subject

Chapter 3 discusses the approximation schemes used to approach lattice statistical models that are not exactly solvable. In addition to the mean field approximation, it also considers the Bethe–Peierls approach to the Ising model. Moreover, there is a thorough discussion of the Gaussian model and its spherical version, both of which are two important systems with several points of interest. A chapter appendix provides a detailed analysis of the random walk on different lattices: apart from the importance of the subject on its own, it explains how the random walk is responsible for the critical properties of the spherical model.

scholarly journals Spatio-Temporal Patterns of Dengue Incidence in Medan City, North Sumatera, Indonesia

2021 ◽  
Vol 6 (1) ◽  
pp. 30
Author(s):  
Ayodhia Pitaloka Pasaribu ◽  
Tsheten Tsheten ◽  
Muhammad Yamin ◽  
Yulia Maryani ◽  
Fahmi Fahmi ◽  
...  
Keyword(s):  
Control Strategies ◽  
Public Health Problem ◽  
Temporal Patterns ◽  
Space Time ◽  
Scan Statistic ◽  
Cold Spots ◽  
Spatio Temporal ◽  
Dengue Control ◽  
And Control ◽  
Time Scan

Dengue has been a perennial public health problem in Medan city, North Sumatera, despite the widespread implementation of dengue control. Understanding the spatial and temporal pattern of dengue is critical for effective implementation of dengue control strategies. This study aimed to characterize the epidemiology and spatio-temporal patterns of dengue in Medan City, Indonesia. Data on dengue incidence were obtained from January 2016 to December 2019. Kulldorff’s space-time scan statistic was used to identify dengue clusters. The Getis-Ord Gi* and Anselin Local Moran’s I statistics were used for further characterisation of dengue hotspots and cold spots. Results: A total of 5556 cases were reported from 151 villages across 21 districts in Medan City. Annual incidence in villages varied from zero to 439.32 per 100,000 inhabitants. According to Kulldorf’s space-time scan statistic, the most likely cluster was located in 27 villages in the south-west of Medan between January 2016 and February 2017, with a relative risk (RR) of 2.47. Getis-Ord Gi* and LISA statistics also identified these villages as hotpot areas. Significant space-time dengue clusters were identified during the study period. These clusters could be prioritized for resource allocation for more efficient prevention and control of dengue.

scholarly journals Evidence-based controls for epidemics using spatio-temporal stochastic models in a Bayesian framework

2017 ◽  
Vol 14 (136) ◽  
pp. 20170386 ◽  
Author(s):  
Hola K. Adrakey ◽  
George Streftaris ◽  
Nik J. Cunniffe ◽  
Tim R. Gottwald ◽  
Christopher A. Gilligan ◽  
...  
Keyword(s):  
Stochastic Models ◽  
Control Strategies ◽  
Functional Model ◽  
Simulated Data ◽  
Citrus Canker ◽  
Bayesian Framework ◽  
Ecological Modelling ◽  
Effective Control ◽  
Temporal Models ◽  
Spatio Temporal

The control of highly infectious diseases of agricultural and plantation crops and livestock represents a key challenge in epidemiological and ecological modelling, with implemented control strategies often being controversial. Mathematical models, including the spatio-temporal stochastic models considered here, are playing an increasing role in the design of control as agencies seek to strengthen the evidence on which selected strategies are based. Here, we investigate a general approach to informing the choice of control strategies using spatio-temporal models within the Bayesian framework. We illustrate the approach for the case of strategies based on pre-emptive removal of individual hosts. For an exemplar model, using simulated data and historic data on an epidemic of Asiatic citrus canker in Florida, we assess a range of measures for prioritizing individuals for removal that take account of observations of an emerging epidemic. These measures are based on the potential infection hazard a host poses to susceptible individuals (hazard), the likelihood of infection of a host (risk) and a measure that combines both the hazard and risk (threat). We find that the threat measure typically leads to the most effective control strategies particularly for clustered epidemics when resources are scarce. The extension of the methods to a range of other settings is discussed. A key feature of the approach is the use of functional-model representations of the epidemic model to couple epidemic trajectories under different control strategies. This induces strong positive correlations between the epidemic outcomes under the respective controls, serving to reduce both the variance of the difference in outcomes and, consequently, the need for extensive simulation.

scholarly journals Spatial Modelling of Within-Field Weed Populations; a Review

Agronomy ◽  
2020 ◽  
Vol 10 (7) ◽  
pp. 1044
Author(s):  
Gayle J. Somerville ◽  
Mette Sønderskov ◽  
Solvejg Kopp Mathiassen ◽  
Helen Metcalfe
Keyword(s):  
Herbicide Resistance ◽  
Weed Management ◽  
Control Strategies ◽  
Management Strategies ◽  
Spatial Modelling ◽  
Integrated Weed Management ◽  
Weed Species ◽  
Invasive Weed ◽  
Temporal Models ◽  
Spatio Temporal

Concerns around herbicide resistance, human risk, and the environmental impacts of current weed control strategies have led to an increasing demand for alternative weed management methods. Many new weed management strategies are under development; however, the poor availability of accurate weed maps, and a lack of confidence in the outcomes of alternative weed management strategies, has hindered their adoption. Developments in field sampling and processing, combined with spatial modelling, can support the implementation and assessment of new and more integrated weed management strategies. Our review focuses on the biological and mathematical aspects of assembling within-field weed models. We describe both static and spatio-temporal models of within-field weed distributions (including both cellular automata (CA) and non-CA models), discussing issues surrounding the spatial processes of weed dispersal and competition and the environmental and anthropogenic processes that affect weed spatial and spatio-temporal distributions. We also examine issues surrounding model uncertainty. By reviewing the current state-of-the-art in both static and temporally dynamic weed spatial modelling we highlight some of the strengths and weaknesses of current techniques, together with current and emerging areas of interest for the application of spatial models, including targeted weed treatments, economic analysis, herbicide resistance and integrated weed management, the dispersal of biocontrol agents, and invasive weed species.

scholarly journals Dynamic evolution of schistosomiasis distribution under different control strategies: Results from surveillance covering 1991–2014 in Guichi, China

2021 ◽  
Vol 15 (1) ◽  
pp. e0008976
Author(s):  
Yi Hu ◽  
Robert Bergquist ◽  
Yue Chen ◽  
Yongwen Ke ◽  
Jianjun Dai ◽  
...  
Keyword(s):  
Prevention And Control ◽  
Control Strategies ◽  
Descriptive Analysis ◽  
Chinese Government ◽  
Cross Sectional ◽  
High Prevalence ◽  
Temporal Model ◽  
Spatio Temporal ◽  
And Control ◽  
The Village

Background Since the founding of the China, the Chinese government, depending on the changing epidemiological situations over time, adopted different strategies to continue the progress towards elimination of schistosomiasis in the country. Although the changing pattern of schistosomiasis distribution in both time and space is well known and has been confirmed by numerous studies, the problem of how these patterns evolve under different control strategies is far from being understood. The purpose of this study is, therefore, to investigate the spatio-temporal change of the distribution of schistosomiasis with special reference to how these patterns evolve under different control strategies. Methodology / Principal findings Parasitological data at the village level were obtained through access to repeated cross-sectional surveys carried out during 1991–2014 in Guichi, a rural district along the Yangtze River in Anhui Province, China. A hierarchical dynamic spatio-temporal model was used to evaluate the evolving pattern of schistosomiasis prevalence, which accounted for mechanism of dynamics of the disease. Descriptive analysis indicates that schistosomiasis prevalence displayed fluctuating high-risk foci during implementation of the chemotherapy-based strategy (1991–2005), while it took on a homogenous pattern of decreasing magnitude in the following period when the integrated strategy was implemented (2006–2014). The dynamic model analysis showed that regularly global propagation of the disease was not present after the effect of proximity to river was taken into account but local pattern transition existed. Maps of predicted prevalence shows that relatively high prevalence (>4%) occasionally occurred before 2006 and prevalence presents a homogenous and decreasing trend over the study area afterwards. Conclusions Proximity to river is still an important determinant for schistosomiasis infection regardless of different types of implemented prevention and control strategies. Between the transition from the chemotherapy-based strategy to the integrated one, we noticed a decreased prevalence. However, schistosomiasis would remain an endemic challenge in these study areas. Further prevention and control countermeasures are warranted.

PHASE DIAGRAMS AND CORRELATION INEQUALITIES OF A THREE-STATE STOCHASTIC EPIDEMIC MODEL ON THE SQUARE LATTICE

2006 ◽  
Vol 16 (12) ◽  
pp. 3687-3693 ◽  
Author(s):  
KAZUMICHI OHTSUKA ◽  
NORIO KONNO ◽  
NAOKI MASUDA ◽  
KAZUYUKI AIHARA
Keyword(s):  
Particle System ◽  
Contact Process ◽  
Mean Field ◽  
Field Approximation ◽  
Correlation Inequalities ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Pair Approximation ◽  
Stochastic Particle System ◽  
Stochastic Epidemic

We study a three-state stochastic particle system on the square lattice, which extends the contact process. The phase diagram is analyzed by the mean-field approximation, the pair approximation, and numerics. The pair approximation turns out to be better than the meanfield ansatz. We also show that the Harris-FKG type correlation inequalities approximately hold in the present model.

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