On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

Optimizing Contact Network Topological Parameters of Urban Populations Using the Genetic Algorithm

This paper explores the application of complex network models and genetic algorithms in epidemiological modeling. By considering the small-world and Barabási-Albert network models, we aim to replicate the dynamics of disease spread in urban environments. This study emphasizes the importance of accurately mapping individual contacts and social networks to forecast disease progression. Using a genetic algorithm, we estimate the input parameters for network construction, thereby simulating disease transmission within these networks. Our results demonstrate the networks' resemblance to real social interactions, highlighting their potential in predicting disease spread. This study underscores the significance of complex network models and genetic algorithms in understanding and managing public health crises.

Spatial dynamics of COVID-19 in São Paulo: A cellular automata and GIS approach

This study examines the spread of COVID-19 in São Paulo, Brazil, using a combination of cellular automata and geographic information systems to model the epidemic's spatial dynamics. By integrating epidemiological models with georeferenced data and social indicators, we analyse how the virus propagates in a complex urban setting, characterized by significant social and economic disparities. The research highlights the role of various factors, including mobility patterns, neighbourhood configurations, and local inequalities, in the spatial spreading of COVID-19 throughout São Paulo. We simulate disease transmission across the city's 96 districts, offering insights into the impact of network topology and district-specific variables on the spread of infections. The study seeks to fine-tune the model to extract epidemiological parameters for further use in a statistical analysis of social variables. Our findings underline the critical importance of spatial analysis in public health strategies and emphasize the necessity for targeted interventions in vulnerable communities. Additionally, the study explores the potential of mathematical modelling in understanding and mitigating the effects of pandemics in urban environments.

A network model of social contacts with small-world and scale-free features, tunable connectivity, and geographic restrictions

Small-world networks and scale-free networks are well-known theoretical models within the realm of complex graphs. These models exhibit "low" average shortest-path length; however, key distinctions are observed in their degree distributions and average clustering coefficients: in small-world networks, the degree distribution is bell-shaped and the clustering is "high"; in scale-free networks, the degree distribution follows a power law and the clustering is "low". Here, a model for generating scale-free graphs with "high" clustering is numerically explored, since these features are concurrently identified in networks representing social interactions. In this model, the values of average degree and exponent of the power-law degree distribution are both adjustable, and spatial limitations in the creation of links are taken into account. Several topological metrics are calculated and compared for computer-generated graphs. Unexpectedly, the numerical experiments show that, by varying the model parameters, a transition from a power-law to a bell-shaped degree distribution can occur. Also, in these graphs, the degree distribution is most accurately characterized by a pure power-law for values of the exponent typically found in real-world networks.

A novel fractional model for the projection of households using wealth index quintiles

Forecasting household assets provides a better opportunity to plan their socioeconomic activities for the future. Fractional mathematical models offer to model the asset-holding data into a piece of scientific evidence in addition to forecasting their future value. This research focuses on the development of a new fractional mathematical model based on the wealth index quintile (WIQ) data. To accomplish the objective, we used the system of coupled fractional differential equations by defining the fractional term with the Caputo derivative and verified it with the stability tests considering the steady-state solution. A numerical solution of the model was obtained using the Adams-Bashforth-Moulton method. To validate the model, we used real-time data obtained from the household series of surveys in Punjab, Pakistan. Different case studies that elucidate the effect of quintiles on the population are also presented. The accuracy of results between real-world and simulated data was compared using absolute and relative errors. The synchronization between the simulated results and real-time data verifies the formulation of the fractional WIQ model. This fractional model can be utilized to predict the approximation of the asset-holding of the households. Due to its relative nature, the model also provides the opportunity for the researchers to use the WIQs of their respective regions to forecast the households' socioeconomic conditions.

Assessing the Impact of Contact Tracing, Quarantine and Red Zone on the Dynamical Evolution of the Covid-19 Pandemic using the Cellular Automata Approach and the Resulting Mean Field System: A Case study in Mauritius

A cellular automaton (CA) depicting the dynamics of the Covid-19 pandemic, is set up. Unlike the classic CA models, the present CA is an enhanced version, embodied with contact tracing, quarantine and red zones to model the spread of the Covid-19 pandemic. The incubation and illness periods are assimilated in the CA system. An algorithm is provided to showcase the rules governing the CA, with and without the enactment of red zones. By means of mean field approximation, a nonlinear system of delay differential equations (DDE) illustrating the dynamics of the CA is emanated. The concept of red zones is incorporated in the resulting DDE system, forming a DDE model with red zone. The stability analysis of both systems are performed and their respective reproduction numbers are derived. The effect of contact tracing and vaccination on both reproduction numbers is also investigated. Numerical simulations of both systems are conducted and real time Covid-19 data in Mauritius for the period ranged from 5 March 2021 to 2 September 2021, is employed to validate the model. Our findings reveal that a combination of both contact tracing and vaccination is indispensable to attenuate the reproductive ratio to less than 1. Effective contact tracing, quarantine and red zones have been the key strategies to contain the Covid-19 virus in Mauritius. The present study furnishes valuable perspectives to assist the health authorities in addressing the unprecedented rise of Covid-19 cases.

Estimates of the collective immunity to COVID-19 derived from a stochastic cellular automaton based framework

In the context of the propagation of infectious diseases, when a sufficient degree of immunisation is achieved within a population, the spread of the disease is ended or significantly decreased, leading to collective immunity, meaning the indirect protection given by immune individuals to susceptible individuals. Here we describe the estimates of the collective immunity to COVID-19 from a stochastic cellular automaton based model designed to emulate the spread of SARS-CoV-2 in a population of static individuals interacting only via a Moore neighbourhood of radius one, with a view to analyze the impact of initially immune individuals on the dynamics of COVID-19. This impact was measured by comparing a progression of initial immunity ratio-the percentage of immunised individuals before patient zero starts infecting its neighbourhood-from 0 to 95% of the initial population, with the number of susceptible individuals not contaminated, the peak value of active cases, the total number of deaths and the emulated pandemic duration in days. The influence of this range of immunities over the model was tested with different parameterisations regarding the uncertainties involved in the model such as the durations of the cellular automaton states, the contamination contributions of each state and the state transition probabilities. A collective immunity threshold of 55 % ± 2.5 % on average was obtained from this procedure, under four distinct parameterisations, which is in tune with the estimates of the currently available medical literature, even increasing the uncertainty of the input parameters.

Spatial dynamics of dengue fever spreading for the coexistence of two serotypes with an application to the city of São Paulo, Brazil

BACKGROUND AND OBJECTIVE

Dengue fever is a disease in which individuals' spatial distribution and Aedes aegypti mosquitoes breeding places are important factors for the disease dynamics. Typically urban, dengue is a problem for least developed countries due to the ineffectiveness in controlling the vector and disorderly urbanization processes. The result is a composition of urban sanitation problems and areas with high demographic densities and intense flows of people. This paper explores the spatial distribution of vector breeding places to evaluate introducing a new dengue serotype to a population at equilibrium for a pre-existing serotype. The paper's objective is to analyze the spatial dynamics of dengue using variations of the basic reproduction number.

METHODS

A model based on probabilistic cellular automata is proposed to permitting the necessary flexibility to consider some spatial distributions of vector breeding places. Then, ordinary differential equations are used as a mean-field approach of the model, and the basic reproduction number (R₀) is derived considering the next-generation matrix method. A spatial approach for R₀ is also proposed, and the model is tested in a neighbourhood from the city of São Paulo, Brazil, to examine the potential risks of vector breeding cells distribution.

RESULTS

The results indicated that the more spread out these places, the higher are the values of R₀. When the model is applied to a neighbourhood in São Paulo, residential areas may boost the infections and must be under public vigilance to combat vector breeding sites.

CONCLUSIONS

Considering the mean-field approximation of the cellular automata model by ordinary differential equations, the basic reproduction number derived returned an estimative of the disease dynamics in the population. However, the spatial basic reproduction number was more assertive in showing areas with a higher disease incidence. Moreover, the model could be easily adapted to be used in real maps enabling simulations closer to real problems.

A complex network model for a society with socioeconomic classes

People's attitudes and behaviors are partially shaped by the socioeconomic class to which they belong. In this work, a model of scale-free graph is proposed to represent the daily personal contacts in a society with three social classes. In the model, the probability of having a connection between two individuals depends on their social classes and on their physical distance. Numerical simulations are performed by considering sociodemographic data from France, Peru, and Zimbabwe. For the complex networks built for these three countries, average values of node degree, shortest-path length, clustering coefficient, closeness centrality, betweenness centrality, and eigenvector centrality are computed. These numerical results are discussed by taking into account the propagation of information about COVID-19.

The Hybrid Incidence Susceptible-Transmissible-Removed Model for Pandemics : Scaling Time to Predict an Epidemic's Population Density Dependent Temporal Propagation

The susceptible-transmissible-removed (STR) model is a deterministic compartment model, based on the susceptible-infected-removed (SIR) prototype. The STR replaces 2 SIR assumptions. SIR assumes that the emigration rate (due to death or recovery) is directly proportional to the infected compartment’s size. The STR replaces this assumption with the biologically appropriate assumption that the emigration rate is the same as the immigration rate one infected period ago. This results in a unique delay differential equation epidemic model with the delay equal to the infected period. Hamer’s mass action law for epidemiology is modified to resemble its chemistry precursor—the law of mass action. Constructing the model for an isolated population that exists on a surface bounded by the extent of the population’s movements permits compartment density to replace compartment size. The STR reduces to a SIR model in a timescale that negates the delay—the transmissible timescale. This establishes that the SIR model applies to an isolated population in the disease’s transmissible timescale. Cyclical social interactions will define a rhythmic timescale. It is demonstrated that the geometric mean maps transmissible timescale properties to their rhythmic timescale equivalents. This mapping defines the hybrid incidence (HI). The model validation demonstrates that the HI-STR can be constructed directly from the disease’s transmission dynamics. The basic reproduction number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}R0) is an epidemic impact property. The HI-STR model predicts that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0 \propto \root \mathfrak{B} \of {\rho_n}$$\end{document}R0∝ρnB where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document}ρn is the population density, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{B}}$$\end{document}B is the ratio of time increments in the transmissible- and rhythmic timescales. The model is validated by experimentally verifying the relationship. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}R0’s dependence on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document}ρn is demonstrated for droplet-spread SARS in Asian cities, aerosol-spread measles in Europe and non-airborne Ebola in Africa.

The co-circulation of two infectious diseases and the impact of vaccination against one of them

An epidemiological model based on probabilistic cellular automaton is proposed to investigate the dynamics of two co-circulating infections. In the model, one of these two diseases compromises the immune response to future infections; however, there is vaccine against this immunosuppressive disease. The goal is to evaluate the impact of the vaccination coverage on the prevalence and on the cumulative deaths associated with both contagious diseases. The performed numerical simulations highlight the importance of vaccination on decreasing morbidity and mortality. The results are discussed from a public health standpoint, by taking into account outbreaks of measles and COVID-19.

A deep learning based surrogate model for the parameter identification problem in probabilistic cellular automaton epidemic models

BACKGROUND AND OBJECTIVE

an accurate estimation of the epidemiological model coefficients helps understand the basic principles of disease spreading. Some studies showed that dozens of hours are needed to simulate the traditional probabilistic cellular automaton (PCA) model, and dozens of hours are spent for a fine-tuning of the system. Here, we propose a deep learning-based surrogate model to mimic a PCA model to reduce the simulations' computational time, maintaining an equivalent precision in the estimates.

METHOD

we consider PCA models based on regular lattices of different sizes to generate training data sets varying the parameters related to individuals' movement in the lattice and the disease infectivity. These parameters are the input variables for training the surrogate model, and the outputs parameters to be fitted are the percentages of susceptible and infected individuals at the steady-state, the basic reproduction number R₀, the peak value and the peak instant of infected individuals, I(τ) and τ, respectively.

RESULTS

The proposed surrogate model can predict all the output variables with a low relative error. The surrogate model's training time is independent of the size of the lattice, and the time for evaluating a solution by the surrogate model is low and independent of the lattice size.

CONCLUSIONS

The surrogate model provides a fast simulation time for a generic Susceptible-Infected-Removed (SIR) model in a PCA, which is helpful for tuning the model before final simulations, supporting the initial search for inverse problems of parameters estimation in SIR models and providing a satisfactory estimation of the output variables for large populations.

A model based on cellular automata to estimate the social isolation impact on COVID-19 spreading in Brazil

Background and objective Many countries around the world experienced a high increase in the number of COVID-19 cases after a few weeks of the first case, and along with it, excessive pressure on the healthcare systems. While medicines, drugs, and vaccines against the COVID-19 are being developed, social isolation has become the most used method for controlling the virus spreading. With the social isolation, authorities aimed to slow down the spreading, avoiding saturation of the healthcare system, and allowing that all critical COVID-19 cases could be appropriately treated. By tuning the proposed model to fit Brazil's initial COVID-19 data, the objectives of the paper are to analyze the impact of the social isolation features on the population dynamics; simulate the number of deaths due to COVID-19 and due to the lack of healthcare infrastructure; study combinations of the features for the healthcare system does not collapse; and analyze healthcare system responses for the crisis. Methods In this paper, a Susceptible-Exposed-Infected-Removed model is described in terms of probabilistic cellular automata and ordinary differential equations for the transmission of COVID-19, flexible enough for simulating different scenarios of social isolation according to the following features: the start day for the social isolation after the first death, the period for the social isolation campaign, and the percentage of the population committed to the campaign. Results Results showed that efforts in the social isolation campaign must be concentrated both on the isolation percentage and campaign duration to delay the healthcare system failure. For the hospital situation in Brazil at the beginning of the pandemic outbreak, a rate of 200 purchases per day of intensive care units and mechanical ventilators is the minimum rate to prevent the collapse of the healthcare system. Conclusions By using the model for different scenarios, it is possible to estimate the impact of social isolation campaign adhesion. For instance, if the social isolation percentage increased from 40% to 50% in Brazil, the purchase rate of 150 intensive care units and mechanical ventilators per day would be enough to prevent the healthcare system to collapse. Moreover, results showed that a premature relaxation of the social isolation campaign can lead to subsequent waves of contamination.

The influence of immune individuals in disease spread evaluated by cellular automaton and genetic algorithm

BACKGROUND AND OBJECTIVE

One of the main goals of epidemiological studies is to build models capable of forecasting the prevalence of a contagious disease, in order to propose public health policies for combating its propagation. Here, the aim is to evaluate the influence of immune individuals in the processes of contagion and recovery from varicella. This influence is usually neglected.

METHODS

An epidemic model based on probabilistic cellular automaton is introduced. By using a genetic algorithm, the values of three parameters of this model are determined from data of prevalence of varicella in Belgium and Italy, in a pre-vaccination period.

RESULTS

This methodology can predict the varicella prevalence (with average relative error of 2%-4%) in these two European countries. Belgium data can be explained by ignoring the role of immune individuals in the infection propagation; however, Italy data can be explained by considering contagion exclusively mediated by immune individuals.

CONCLUSIONS

The role of immune individuals should be accurately delineated in investigations on the dynamics of disease propagation. In addition, the proposed methodology can be adapted for evaluating, for instance, the role of asymptomatic carriers in the novel coronavirus spread.

Clustered Breeding Sites: Shelters for Vector-Borne Diseases

Here, the propagation of vector-borne diseases is modeled by using a probabilistic cellular automaton. Numerical simulations considering distinct spatial distributions and time variations of the vector abundance are performed, in order to investigate their impacts on the number of infected individuals of the host population. The main conclusion is as follows: in the clustered distributions, the prevalence is lower, but the eradication is more difficult to be achieved, as compared to homogeneous distributions. This result can be relevant in the implementation of preventive surveillance measures.

Disease spreading in complex networks: A numerical study with Principal Component Analysis

Disease spreading models need a population model to organize how individuals are distributed over space and how they are connected. Usually, disease agent (bacteria, virus) passes between individuals through these connections and an epidemic outbreak may occur. Here, complex networks models, like Erdös-Rényi, Small-World, Scale-Free and Barábasi-Albert will be used for modeling a population, since they are used for social networks; and the disease will be modeled by a SIR (Susceptible-Infected-Recovered) model. The objective of this work is, regardless of the network/population model, analyze which topological parameters are more relevant for a disease success or failure. Therefore, the SIR model is simulated in a wide range of each network model and a first analysis is done. By using data from all simulations, an investigation with Principal Component Analysis (PCA) is done in order to find the most relevant topological and disease parameters.

Stability Analysis of SIR Model with Distributed Delay on Complex Networks

In this paper, by taking full consideration of distributed delay, demographics and contact heterogeneity of the individuals, we present a detailed analytical study of the Susceptible-Infected-Removed (SIR) epidemic model on complex population networks. The basic reproduction number [Formula: see text] of the model is dominated by the topology of the underlying network, the properties of individuals which include birth rate, death rate, removed rate and infected rate, and continuously distributed time delay. By constructing suitable Lyapunov functional and employing Kirchhoff's matrix tree theorem, we investigate the globally asymptotical stability of the disease-free and endemic equilibrium points. Specifically, the system shows threshold behaviors: if [Formula: see text], then the disease-free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally asymptotically stable. Furthermore, the obtained results show that SIR models with different types of delays have different converge time in the process of contagion: if [Formula: see text], then the system with distributed time delay stabilizes fastest; while [Formula: see text], the system with distributed time delay converges most slowly. The validness and effectiveness of these results are demonstrated through numerical simulations.

Dynamic Cellular Automata Based Epidemic Spread Model for Population in Patches with Movement

Epidemiology is the study of spread of diseases among the group of population. If not controlled properly, the epidemic would cause an enormous number of problems and lead to pandemic situation. Here in this paper we consider the situation of populated areas where people live in patches. A dynamic cellular automata model for population in patches is being proposed in this paper. This work not only explores the computing power of cellular automata in modeling the epidemic spread but also provides the pathway in reduction of computing time when using the dynamic cellular automata model for the patchy population when compared to the static cellular automata which is used for a nonpatchy homogeneous population. The variation of the model with movement of population among the patches is also explored which provides an efficient way for evacuation planning and vaccination of infected areas.

Stability analysis of a novel epidemics model with vaccination and nonlinear infectious rate

In this paper, by considering pathogen evolution and human interventions behaviors with vaccines or drugs, we build up a novel SEIRW model with the vaccination to the newborn children. The stability of the SEIRW model with time-varying perturbation to predict the evolution tendency of the disease is analyzed. Furthermore, we introduce a time-varying delay into the susceptible and infective stages in the model and give some global exponential stability criteria for the time-varying delay system. Finally, numerical simulations are presented to verify the results.

Moment approximation of infection dynamics in a population of moving hosts

The modelling of contact processes between hosts is of key importance in epidemiology. Current studies have mainly focused on networks with stationary structures, although we know these structures to be dynamic with continuous appearance and disappearance of links over time. In the case of moving individuals, the contact network cannot be established. Individual-based models (IBMs) can simulate the individual behaviours involved in the contact process. However, with very large populations, they can be hard to simulate and study due to the computational costs. We use the moment approximation (MA) method to approximate a stochastic IBM with an aggregated deterministic model. We illustrate the method with an application in animal epidemiology: the spread of the highly pathogenic virus H5N1 of avian influenza in a poultry flock. The MA method is explained in a didactic way so that it can be reused and extended. We compare the simulation results of three models: 1. an IBM, 2. a MA, and 3. a mean-field (MF). The results show a close agreement between the MA model and the IBM. They highlight the importance for the models to capture the displacement behaviours and the contact processes in the study of disease spread. We also illustrate an original way of using different models of the same system to learn more about the system itself, and about the representation we build of it.

The failure of R0

The basic reproductive ratio, R(0), is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R(0) < 1, the disease dies out, whereas if R(0) > 1, the disease persists. R(0) has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, R(0) is flawed. Diseases can persist with R(0) < 1, while diseases with R(0) > 1 can die out. We show that the same model of malaria gives many different values of R(0), depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of R(0) for a variety of diseases, and examine some of the alternatives that have been proposed. If R(0) is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.

Modeling the dynamic transmission of dengue fever: investigating disease persistence

BACKGROUND

Dengue is a disease of great complexity, due to interactions between humans, mosquitoes and various virus serotypes as well as efficient vector survival strategies. Thus, understanding the factors influencing the persistence of the disease has been a challenge for scientists and policy makers. The aim of this study is to investigate the influence of various factors related to humans and vectors in the maintenance of viral transmission during extended periods.

METHODOLOGY/PRINCIPAL FINDINGS

We developed a stochastic cellular automata model to simulate the spread of dengue fever in a dense community. Each cell can correspond to a built area, and human and mosquito populations are individually monitored during the simulations. Human mobility and renewal, as well as vector infestation, are taken into consideration. To investigate the factors influencing the maintenance of viral circulation, two sets of simulations were performed: (1(st)) varying human renewal rates and human population sizes and (2(nd)) varying the house index (fraction of infested buildings) and vector per human ratio. We found that viral transmission is inhibited with the combination of small human populations with low renewal rates. It is also shown that maintenance of viral circulation for extended periods is possible at low values of house index. Based on the results of the model and on a study conducted in the city of Recife, Brazil, which associates vector infestation with Aedes aegytpi egg counts, we question the current methodology used in calculating the house index, based on larval survey.

CONCLUSIONS/SIGNIFICANCE

This study contributed to a better understanding of the dynamics of dengue subsistence. Using basic concepts of metapopulations, we concluded that low infestation rates in a few neighborhoods ensure the persistence of dengue in large cities and suggested that better strategies should be implemented to obtain measures of house index values, in order to improve the dengue monitoring and control system.

The trend towards habitat fragmentation is the key factor driving the spread of Crimean-Congo haemorrhagic fever

We aimed to characterize an environmental niche driving the distribution of Crimean-Congo haemorrhagic fever (CCHF) in Turkey, using a geo-referenced collection of cases reported between 2003 and 2008 and a set of climate and vegetation features. We used mean monthly air temperatures and Normalized Derived Vegetation Index (NDVI) values, at a resolution of 0.1 degrees , as well as climate features at and below the surface. We computed significant differences in monthly variables between positive and negative sites, within the range of distribution of the tick vector. Seasonal climate (growth season and summer length, accumulated temperatures in winter) and vegetation components (anomalies in NDVI data) were analysed. Fragmentation of habitat was obtained from NDVI monthly data at a resolution of 1 km. Neither single climate or vegetation variables, nor any individual seasonal component, accounted in both space and time for the delineation of areas of disease although accumulated temperatures in winter consistently showed lower values in areas where the disease was reported. Coherent and significant differences between disease-containing and disease-free sites were found when habitat fragmentation and connectivity were examined. High fragmentation and connectivity were unambiguously associated with sites where disease is reported and accounted for the spatial spread of cases in 2003-2008. CCHF cases were always associated with areas of highly fragmented and well-connected patches within the range of the tick vector, while there were no reports from areas with low fragmentation. There was a linear relationship between degree of fragmentation and case incidence. The implications of these findings are discussed with reference to the concept of disease spread through networks of connected spots with high densities of infected vectors and social factors driving different human activities in sites of high fragmentation.