The authors have declared that no competing interests exist.
Conceived and designed the experiments: PS WS CS. Performed the experiments: PS WS CS. Analyzed the data: PS WS CS. Contributed reagents/materials/analysis tools: PS WS CS. Wrote the paper: PS WS CS.
Various epidemics have arisen in rural locations through humananimal interaction, such as the H1N1 outbreak of 2009. Through collaboration with local government officials, we have surveyed a rural county and its communities and collected a dataset characterizing the rural population. From the respondents’ answers, we build a social (facetoface) contact network. With this network, we explore the potential spread of epidemics through a SusceptibleLatentInfectedRecovered (SLIR) disease model. We simulate an exact model of a stochastic SLIR Poisson process with disease parameters representing a typical influenzalike illness. We test vaccine distribution strategies under limited resources. We examine global and locationbased distribution strategies, as a way to reach critical individuals in the rural setting. We demonstrate that locations can be identified through contact metrics for use in vaccination strategies to control contagious diseases.
In general, the spread of infectious diseases can be contained by human response using different approaches. Susceptible people can acquire immunization through vaccination, or can protect themselves from the diseases using preventive behaviors, such as avoiding close physical contacts with infected individuals or using hygienic habits. Correspondingly, human responses can be modeled using three classes of models distinguished by changes taking place in compartments, parameters, or contact levels to take into account the behavioral changes
A vast literature exists on efficient vaccination strategies, given the need for efficient strategies to distribute vaccines that can often be insufficient for the entire population. Some of these strategies assume that human contact networks are well represented by scale free networks. One popular strategy aims at immunizing those individuals having the highest number of contacts, as the most critical actors for spreading the infection
In any case, assessing the effectiveness of mitigation strategies and behavioral responses both from a public health point of view and from individuals’ perspectives is a complex and not fullyexplored problem. In particular, a thorough evaluation and comparison of feasible mitigation strategies in the specific setting of rural regions is missing. In other words, not only the amount of success a given strategy can provide is not determined, but also its related cost in economical and social terms is unknown.
In this paper, we carry out extensive simulations on a weighted contact network determined by collected data in the City of Chanute and Neosho County in the State of Kansas. In particular we study the impact of limited resource vaccination campaigns, using an exact model of a stochastic SLIR Poisson process. Simulations are run across several scenarios and with stochastic sets of the SLIR model parameters. The evaluation of the vaccination campaigns is performed computing the average number of cases prevented per a single vaccine and the sizes and durations of the outbreaks. Our contributions are twofold: we construct and analyze a databased rural contact network and we provide a thorough analysis and comparison of mitigation strategies in a rural region. We hope that our results can provide practical guidelines for health officials to contain and suppress epidemics in rural regions.
In the following we describe the data collection and analysis, and the models for the network, for the epidemic spreading, and also for vaccination strategies and distributions.
As of the 2010 U.S. Census, Neosho County was a rural county with 16,512 residents in 571.5 square miles in southeastern Kansas. Most of the population was White (94.1%); a majority were female (50.6%) and many (17.4%) were 65 years of age or older. The median household income was $36,702 with 17.0% living below the poverty level. Between July and October 2010, the towns of Chanute, Thayer, and Galesburg were selected to participate in a survey concerning factors that would predict the spread of epidemics in rural areas. From county public household rosters, households were randomly selected from Chanute (10%, N = 171), Thayer (50%, N = 158), and Galesburg (50%, N = 73) for a total initial
The tailored design method was used, with minor modifications, to improve response rates
A majority (56%) of the respondents reported being from Chanute compared to 23% from Thayer and 10% from Galesburg (the remaining percentage did not specify exactly where they were from). Of the 357 participants, the largest number were ages 45 to 64 (47.1%), with 26.1% 65 years of age or older and 18.8% (26–44) and 8.1% (18 to 25) younger than 45. A majority of the participants were females (57.6%). Most of the respondents (75.4%) had lived in their local community for 15 years or more. The vast majority (97.5%) of the respondents lived in a single family home. Very few (6.2%) of the households included a homebound member. Most of the respondents had either the equivalent of a high school degree (22%) or a college (23%) or graduate (12%) degree. Nearly sixty percent had incomes between $25,000 and 100,000 a year with 11% earning more and 30% earning less. Some respondents had type I (1.2%) or type II diabetes (10.4%) or were prediabetic (3.2%). Most respondents considered themselves to be slightly (35.7%), somewhat (18.2%), or extremely (8.6%) overweight. Most (56.6%) reported that they ate out one or two times a week with 26% eating out more often and 17% not at all.
In terms of compliance risk, nearly 49% of respondents said they would still visit at least one or two households outside of their home if there was a serious epidemic and radio/TV/internet had told them to remain at home and not visit with others.
The distribution of the number of households that a respondent expects to still visit in a week against advice during a serious epidemic is shown.
The distribution of types of animals a respondent interacts with in a typical day is shown. Note that the total does not sum to one as respondents can interact with multiple types of animals.
Here, the procedure to construct the contact network from survey data is explained. Furthermore, the compartmental model used for simulations and the preemptive vaccination strategies are described.
From the survey responses, we constructed a rural contact network as an estimation of the social contact structure among the survey respondents. The network is based on two central questions: the number of contacts that a person has, and the locations that a person visits at different times in a typical day. The basis for the interactions between a pair of respondents is the locations that they both visited in common. We considered 4 types of locationbased interactions: both visit the same location in the morning, both visit the same location in the afternoon, both visit the same location in the evening, and both visit the same location regardless of time. The fourth category introduces some overlapping in the interactions, but it is added to account for some of the uncertainty in potential pathways of the disease spread. We considered 66 locations in the network construction and therefore 264 = 66×4 possible interactions between each pair of survey respondents. We compute normalized weights from each respondent
Six of the vaccination strategies will center on three node metrics: incoming node strength (the sum of the weights incoming to a node), outgoing node strength (the sum of the weights outgoing from a node), and node betweenness (a count of the shortest paths among all pairs that utilize the node)
A depiction of the rural contact network developed from a survey of Neosho County is shown, where the individuals are represented by purple nodes in a “cloud,” which is connected by the respondents local travel habits to the set of rural locations shown in orange on the map.
On this weighted network, we model an epidemic outbreak using a SusceptibleLatentInfectedRecovered compartmental model (SLIR)
We simulate this model exactly using an eventdriven simulation of the SLIR process on the weighted rural contact network. We initialize the simulation by assigning a disease state to each node and then drawing exponential waiting times for the next event at each node. Taking the event with the minimum time across all nodes, we advance the event node to its next disease state and redraw waiting times for all nodes. This step is repeated until all waiting times are infinite, which happens when the disease process is complete. At this point, all nodes will be either susceptible or recovered. In the eventdriven simulation, the time periods between successive events will not be regular, but instead they are noninteger stochastic values.
Vaccination is carried out by selecting a set of nodes and immunizing them with a certain vaccine efficacy rate. We consider seven different strategies for selecting the set of nodes for vaccination. The first and simplest strategy is a random selection of 10% of the population (35 nodes). The random method represents a blind distribution across the population. The next three strategies consider a targeted selection of nodes (individuals) based respectively on the three node metrics, incoming node strength, outgoing node strength, and node betweenness. These three strategies are idealistically implemented by selecting the 35 nodes with the highest values for the respective metric and administering the vaccine. For less ideal situations, we consider three additional strategies that attempt to represent feasible vaccine distribution strategies for rural populations. Considering again the three above mentioned network metrics, we determine the location which has the highest average value (on the set of nodes that visit the location) of each metric. These locations are a restaurant (outgoing node strength), a pharmacy (node betweenness), and a location used for public events (incoming node strength). After selecting the locations that represent on average the best places to find nodes with higher values of each metric, we consider a random selection within a location of 10% of the entire population for vaccination. This locationbased targeting has been proposed in
Orange nodes represent locations, red circles represent the selected nodes for vaccination, and the green nodes represent random selected individuals, whose friends will be candidate for vaccination.
We measured on the network the metrics of interest for the vaccination targeting strategies.
Note that the vertical axis has a log scale.
(Left) A visualization of the rural community contact network showing the nodes and the links having weights between 0.2 and 1.0, where the weights of the green links are between 0.2 and 0.3 and those of the purple links are between 0.3 and 1.0. (Right) A visualization of the rural community contact network showing the nodes and the links having weights between 0.4 and 1.0 as well as the “bestfriends” links, where the best friend link of a node is defined as the link having the highest outgoing weight.
Note that the vertical axis has a log scale.
Note that the vertical axis has a log scale.
In general, while many of these relationships are not especially strong in terms of effect sizes, it appears that residents with higher levels of education, who have longer commutes, who are younger, with more income, those without diabetes or recent flulike illnesses, who are away from home more hours each day, and who eat out more often are more likely to be important agents in the network measures that influence the potential spread of epidemics. It is interesting to observe that the younger rural residents are likely the most important agents when considering that rural regions are typically characterized by aging populations. This importance appears to be due to them, the younger persons, spending more time away from home, driving longer to work, visiting more businesses, and in all this, having and visiting more persons outside of their homes. Perhaps, the traditional farmer who rarely visits town and is mostly selfsufficient within his home and immediate neighbors is giving way to a younger generation and changing economy where increased travel and social interaction are increasingly required.
We performed extensive simulations to investigate potential epidemics and the proposed vaccination strategies for the rural contact network representing a sample population from Neosho County. To mimic a realistic epidemic with the stochastic SLIR model, we utilize average values of
For each simulation, we track the numbers of nodes in each disease state through time as well as the timings of all event occurrences. We capture the total cases, representing this as the attack rate or the fraction of the total population infected, and the duration of each outbreak in days. The duration of an outbreak is the (continuous) time in days from the beginning of the simulation to the recovery (I to R transition) of the last infected node at which point all nodes in the network will either be susceptible or recovered. We define an outbreak as any trial that resulted in at least one secondary infection and present statistics only over the trials successfully demonstrating outbreaks. We simplify the presentation of the results of the second type of experiment by computing and plotting the average and 95% range of the resulting total cases for each group of 10,000 simulations on a single
The distributions of the total cases as a fraction of the considered population over the estimated range of
We ran seven sets of simulations to consider the seven vaccination strategies described in Section 3 and for each set we ran both types of experiments as described previously. In each trial, we draw a value for vaccine efficacy from a Gaussian distribution with mean of 72.0% and standard deviation of 6.0% to approximate realistic efficacy values
The distributions of the total cases as a fraction of the considered population over the estimated range of
The three idealistic vaccination strategies select their targets and vaccinate them by rankings determined by the node metrics. The left side of
(Left) Under a nodebetweennessbased
A brief comparison of the results shown in
The comparison of no mitigation (No Vacc, blue line), a random vaccination of 10 percent of the population (Random, green line), nodebetweennessbased
Average  Median  95% CI  
No Vaccination  0.0512  0.0142  (0.0057, 0.3088) 




Random Vaccination  0.0407  0.0113  (0.0057, 0.2493) 




Targeted Betweenness  0.0251  0.0113  (0.0057, 0.1388) 




Targeted Instrength  0.0324  0.0113  (0.0057, 0.1955) 




Targeted Outstrength  0.0261  0.0113  (0.0057, 0.1445) 




Location Targeted Betweenness  0.0433  0.0113  (0.0057, 0.2635) 




Location Targeted Instrength  0.0433  0.0113  (0.0057, 0.2635) 




Location Targeted Outstrength  0.0434  0.0113  (0.0057, 0.2635) 



The last column of
Probability of outbreak  Cases Prevented Per Vaccine  
No Vaccination  0.3928  — 
Random Vaccination  0.3783  0.1065 
Targeted Betweenness  0.3742  0.2638 
Targeted Instrength  0.3623  0.1898 
Targeted Outstrength  0.3768  0.2537 
Location Targeted Betweenness  0.3778  0.0797 
Location Targeted Instrength  0.3783  0.0795 
Location Targeted Outstrength  0.3776  0.0790 
From the network analysis, we observed that the rural contact structure displays a significant amount of heterogeneity in the considered metrics. This heterogeneity suggests that the small number of nodes having the highest values of each metric might present strategic subpopulations for mitigation objectives. The rural contact network also contained a relatively diseaseresistant subpopulation due to their poor level of connectivity and location on the “fringes” of the rural community network. From statistical correlations, it appears that residents with higher levels of education, who have longer commutes, who are younger, with more income, those without diabetes or recent flulike illnesses, who are away from home more hours each day, and who eat out more often are more likely to be important players in the according to the network metrics that influence the potential spread of infectious diseases.
In the data collected from the rural survey, there remain significant limitations. Although the survey presents a variety of types of locations such as schools, restaurants, libraries, and public attractions, the data does not sufficiently capture the information regarding household interactions. It was not feasible to anonymously identify individual households and which survey respondents visited them with the resources at our disposal. The lack of information regarding young respondents and household interactions remains a strong limitation in the characterization of this community and the following epidemic study on the rural contact network.
For vaccine distribution we considered seven strategies, but only four are reasonably feasible for local administrators to implement, those being the random distribution across the population and the three locationbased distributions. The traditional targeted groups for distribution such as the healthcare personnel, the very young (6–59 months), the elderly (50 years or older), pregnant women, those with chronic health issues, and American Indians are not completely identifiable from our survey results
Interestingly, using the network metrics to select locations does not necessarily produce intuitive results. The restaurant chosen to represent locations that are frequented by nodes with high node outgoing node strength (as it had the highest average value) had less than onethird of the survey respondents frequenting it than some of the more popular restaurants in the region. Although diseases are partially mitigated, there is a limit to the reduction that can be observed in the total cases for the strongest diseases due to the resource limitation. Therefore when considering limitedresource vaccine distribution, local administrators should probably follow the traditional priority schedule. However, the identification of the critical locations would be useful for preventative education efforts, realtime epidemic alerts, and emergency resource distribution.
The results of this analysis are intended to help guide responses to a rural epidemic threat. With this, responders can explore the theoretical impacts that might be had from a limitedresource vaccine distribution by exploring various locations for distribution. Social behavior and human interaction (contact) are not exact sciences, so the theoretical mitigation results should be considered possibilities and aspirations rather than deterministic outcomes for any rural county or town.
Starting with a survey of a rural community, demographics were analyzed and an estimation of the social contact structure was built. This network was measured and the metrics were correlated with various demographics from the survey. Through the use of an exact model of a stochastic SLIR Poisson process, we have characterized a typical influenzalike outbreak in the community and investigated vaccination strategies. When considering resourcelimited vaccine distribution strategies, we identified critical locations for ethical targeting subpopulations with the goal of effective disease prevention. Our aspiration is that this analysis will be a valuable resource for both the rural community on which this study focused, and also for several similar communities in the region.
The authors would like to thank Steven Kubler and other officials of the City of Chanute for helpful discussion and information. Publication of this article was funded in part by the Kansas State University Open Access Publishing Fund.