Spatial modeling in disease epidemic studies

By Avishek Majumder & Chandrika Kapagunta on October 3, 2017

Epidemiology of infectious diseases often requires geographical information. Both spatial and temporal factors of a population can affect disease spread. Spatial factors refer to the geographical or topological factors associated with a disease. Temporal factors mean time-bound progress of a disease in a population. These factors influence the virulence of the disease, patterns of prevalence and also future incidents. Temporal factors in disease epidemiology influence the progress of a disease in the population. They also offer clues on the source of the disease and its associated risk factors. However, spatial information of a disease can strongly predict disease prevalence. This is done by linking climate and environmental information to disease prevalence patterns. Statistical models like spatial models can determine risk factors, causality and predict future trends. Therefore, this article discusses the role of spatial modelling in disease epidemiology.

Use of spatial modelling in identifying the spatial structure of diseases

The study of geographical variations of a disease or risk factors is known as spatial epidemiology (Ostfeld, Glass, & Keesing, 2005). Several spatial methods and models have been adopted in epidemiology. Combination of spatial and temporal factors along with multilevel data is known as spatial modelling. It refers to statistical and mathematical modelling of spatial data related to diseases due to its ability to help link secondary factors to distribution trends in a population. Therefore, the underlying spatial structure of disease data can be identified and used to devise control strategies.

Need for spatial modelling in epidemiology

Spatial or geographical data is often stored in the form of a Geographical Information System (GIS) data. It provides information on the location of a disease event. The location is shared in the form of latitude or longitude coordinates and village or district level data. Distances between host-vector-pathogens influence the rate and extent of disease spread. Moreover, spatial information can also provide information on host-vector-pathogen interactions (Ostfeld et al., 2005). Therefore, spatial information is crucial in epidemiology.

Interaction data can also help in designing disease control strategies and predicting future epidemics. Here secondary factors like socioeconomic factors, environmental and climate factors are control factors (Martins & Rocha, 2012). Since spatial epidemiology data are often discrete, the spatial heterogeneity of an epidemic can be quantified (Lambin et al, 2010). Furthermore, using spatial modelling, locations of other factors (environment, pollutant, pathogen etc.) can be connected to disease incidents. Inference on possible risks to the disease can be drawn based on the findings. Finally, it enables isolation of factors contributing to this heterogeneity as well as predicting future disease trends.

Goals of spatial modeling in disease epidemiology (Martins & Rocha, 2012).
Goals of spatial modelling in disease epidemiology (Martins & Rocha, 2012).

Difference between spatial modelling and mechanistic models

Furthermore, infectious disease research adopted mechanistic models. In such models, spatial information was treated as constant. However, there is a need to represent spatial data of diseases as a variable. Dynamic influence on the mode and trends of disease spread aid this supposition (Linard & Tatem, 2012). Therefore, spatial modelling of disease epidemics, also known as spatial epidemiology came into being. Spatial epidemiology has been defined as “the study of spatial variation in disease risk or incidence” (Ostfeld et al., 2005). In spatial epidemiology, statistical modelling in the form of spatial or spatial modelling is an important tool. Furthermore, it helps identify influential factors and their relationship with disease prevalence in a population.

Spatial epidemic models

Several types of spatial models exist, depending on the purpose of the study. These are exploring data, inferring from data and predicting future disease patterns. These methods can also be grouped based on three spatial perspectives where disease information can be analysed and applied (Robb, Bauer, & Vena, 2016). This is represented in the figure below.

Types of spatial epidemic models (Robb, Bauer, & Vena, 2016)
Types of spatial epidemic models (Robb, Bauer, & Vena, 2016).

In traditional methods, disease data is quantified to understand the trends. In Acute event methods, the disease data is understood better during epidemics to create control strategies. Thus, both methods subsequently assist in applying knowledge at the community level.

Types of spatial methods based on epidemiological perspectives (Robb, Bauer, & Vena, 2016)
Types of spatial methods based on epidemiological perspectives (Robb, Bauer, & Vena, 2016)

Statistical models under spatial modelling

Depending on the data scale and the purpose of analysis, Moise, Cunningham, & Inglis, (2015) have described several important methods. These are represented in the table below. Furthermore, Methods applied for describing or exploring data is different from those for predicting patterns.

No. Type of Analysis Method Purpose
Exploratory or descriptive analysis
  Global Patterns
  Quadrant count analysis Description of disease features
  Nearest Neighbour analysis
  Ripley’s K-function
  Local Patterns
  Hot Spot Analysis Mapping of Clusters
  Anselin’s local indicators of spatial association (LISA)
  Kulldorff’s Scan Statistic
Predictive Spatial Patterns
  Voronoi (Thiessen) polygons Prediction of Spatial Patterns
  Inverse Distance Weighting (IDW)
  Kernel Density Estimation (KDE)
  Disease Mapping  
  Disease Clustering  
  Ecological Analysis  

 Types of spatial analysis methods using GIS information (Moise et al., 2015)

Standard techniques are available to analyse data. However, researchers devise new methods to analyse data better. This depends upon the purpose of the study and the limitations of existing models. As a result, researchers are continuously developing a large number of models.

A systematic review of spatial models developed

Different authors have conducted spatial epidemiological studies for infectious diseases. Various models and methods have been applied in the process. Some of them have been reviewed below.

No. Model name Disease under study Geographic region Variables studied Results
1 Logistic Regression model (Kleinschmidt, Bagayoko, Clarke, Craig, & Le Sueu, 2000). Malaria Africa Climatic, population and  topographic. Residual spatial patterns reduced, and residual spatial dependence modelled by kriging. The end predictions made sense from an entomological perspective.
2 Global K-Functions  (Getis, Morrison, Gray, & Scott, 2003). Dengue   Age, poverty, education and household income. Adults clustered strongly within houses and weakly to a distance of 30 meters beyond the household.Clustering not detected beyond 10 meters for positive containers or pupae.
3 Spatial regression model in Bayes.X (Kazembe, 2007). Malaria Northern Malawi Age, environmental factor, altitude, precipitation and soil water capacity. Malaria risk increased with altitude, precipitation, and soil water capacity.
4 Fixed Effects Grouped Logistics Regression model and Bayesian Space-Time Multivariate model (Pullan et al., 2011). Helminths Kenya The age range of sampled individuals, a method of diagnosis, environmental and covariates. In 2009, high certainty that endemicity was below the 20% threshold, helminths prevalence decreased over time and approximately 2.8 million school-age children were living in endemic districts.
5 Spatial explicit model in R (Hagenlocher & Castro, 2015). Malaria United Republic of Tanzania environmental, socioeconomic, demographic, biological, cultural, and political factors. Malaria risk was higher in Mainland areas than in Zanzibar, which is a result of differences in both malaria entomological inoculation rate and prevailing vulnerabilities.
6 Agent-based model in SaTScan  (Pizzitutti et al., 2015). Malaria Peruvian Amazon Age , human, mosquitoes species  and environmental factor- climate. Able to reproduce the variations of the malaria monthly incidence over a period of 3 years and also the spatial heterogeneities of local scale malaria transmission.

A systematic review of spatial models in Infectious disease research

The table above shows that for a single disease (Malaria), different models are applicable since the aims are different. These models can be tested in different software. Each software has different properties and advantages. Also, each of these models has used different ranges of variables. These variables represent demographic profile, environmental factors, socioeconomic factors and disease features.

Spatial modelling for better strategy formulation

Overall, spatial modelling of infectious diseases can be conducted using different statistical models and methods. The methods depend on the purpose of the study and the data available. Future spatial studies of infectious diseases can gain from a wide range of GIS tools developed. More statistical tools are being continuously developed to ensure maximum capture of information from the available data. They highlight the underlying causes and relationships between elements of the data. Consequently, such information will help in a faster analysis of patterns and risks and hence contribute to the better design of control strategies.


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