A Network Control Theory Approach to Modeling and Optimal Control of Zoonoses: Case Study of Brucellosis Transmission in Sub-Saharan Africa
[['Zoonoses–infectious diseases that can be transmitted to humans from other animals–incur significant cost though their impact on both agricultural production and human communities .', 'Zoonoses have particular prevalence and impact in the developing world , where low-cost yet effective strategies for their control and eventual eradication are badly needed ( e . g . , [1] , [2] ) .', 'Control of these zoonoses can be quite challenging , requiring', '1 ) understanding ( and sometimes new development ) of the surveillance , vaccination , and treatment capabilities of a particular zoonotic agent in human and/or animal populations;', '2 ) recognition/modeling of the mechanisms and rates of spread in each species and between species;', '3 ) cooperation across animal- and public health sectors; and', '4 ) the ability to build the infrastructures needed for control within the limitations imposed by the financial and societal circumstances of the community .', 'Historically , infectious disease specialists in collaboration with governmental organizations have attempted to develop effective control and eradication strategies gradually , using field experience that is unique to the region and disease .', 'A particular challenge in controlling zoonotic infections in this way is to appropriately characterize the animal-human interface that leads to spread , and in turn to appropriately allocate resources in the multi-species system .', 'Recently , several studies have demonstrated that mathematical modeling can aid practitioners in developing control strategies , by allowing a priori comparison of the effectiveness of various control strategies and making explicit the roles played by various species in the spread of the disease ( e . g . , [3]–[5] ) .', 'However , efforts to study control of zoonoses using mathematical models remain incomplete .', 'The models used are largely very abstract , often representing animal and/or human populations as a single homogeneous group .', 'Additionally , the current efforts typically only compare a few possible control strategies rather than suggesting a comprehensive design for achieving optimal and robust surveillance and control .', 'Network modeling of infection spread has been a particular area of burgeoning interest over the last few years , see the articles [6]–[12] for a few representative samples .', 'The network ( or , equivalently multi-group- or metapopulation- ) modeling paradigm for infectious diseases builds on the classical compartmental models for disease spread in homogeneous populations ( e . g . , [13] ) ; the network viewpoint was motivated specifically by the recognition that spread patterns are often structured and variable rather than homogeneous , and that control capabilities are targeted .', "Quite a wide range of analyses have been achieved for network spread models , with a particular focus on understanding the role played by the network's topological structure in its spread dynamics .", 'The network spread models have also served as a context for evaluating practical targeted control schemes [8] , [14] .', 'Recently , our group has studied heterogeneous control resource allocation in multi-group ( network ) models for virus spread [14] .', 'This study , as well as analogous efforts on controlling human-engineered networks such as traffic networks [15] , show how targeted controls can be designed for high performance .', 'That is , via analytical means , they identify certain parts of networks ( e . g . , certain individuals , sub-populations , or control capabilities ) that have disproportionate impact on spread , and so suggest concentration of control resources on these components of the network .', 'While such insights regarding control seems germane to mitigation of zoonoses , our results as yet have only been developed using generic models for transmission and control and have only measured spread in terms of one measure ( the basic reproductive number ) , have not considered surveillance at all .', 'Models for zoonotic diseases ( including for brucellosis ) classically have been simple compartmental models rather than network-structured models , with each compartment capturing homogeneous transmission within an entire species , or perhaps for an age group of that species ( e . g . , [3]–[5] ) .', 'Very recently , models for zoonotic infections that capture the detailed spatial or community structure of transmission have been proposed ( e . g . , [10]–[12] ) .', 'These models have allowed characterization of the role of the community structure in spread , as well as comparison of plausible control strategies ( largely via simulation ) ; however , these efforts do not permit systematic analytical design of high-performance control strategies .', 'The purpose of this study is to give a comprehensive treatment of the modeling , surveillance , and cost-effective control of zoonoses , by bringing to bear and enhancing a network-control-theory approach to virus-spread control .', 'As a specific case study , we explore modeling and design of surveillance and control for brucellosis in a prototypical agricultural setting in a resource-constrained area such as sub-Saharan Africa .', "To this end , a network model for brucellosis transmission among animal herds and to human populations is developed , that captures the mechanism of transmission of this zoonotic bacterium , allows repesentation of realistic surveillance and control mechanisms and their costs , and measures the performance of the control scheme with regard to the disease's financial and societal impact .", 'Once the model has been formulated in a general way , we discuss approaches for inferring important network-model parameters from limited experimental data , which include both simple heuristic approaches and new network-estimation tools from the control sciences .', 'Using the parametrized models , design of surveillance and control capabilities is pursued , with the aim of suggesting good targeted control/surveillance strategies as well as improvements to existing strategies .', 'A particular focus of the design is to obtain simple insights into high-performance strategies that do not rely on model details , so that the developed strategies are in some measure robust to inaccuracies and limitations in the models and available data .', 'This study advances the existing efforts on network modeling of infection spread , including our own earlier work , in several ways .', 'First , it makes explicit the grapical modeling of spread in multiple species/breeds using a layered network structure .', 'Second , it carefully models a family of surveillance and control capabilities for zoonoses , and brings to bear a network control theory methodology to comprehensively design the spread control capabilities .', 'This network control theory approach is valuable , because it permits systematic design of multiple control and surveillance capabilities in a multi-faceted network , to meet multiple performance criteria or optimize a performance measure .', 'We believe that this comprehensive design capability is of central importance for the zoonotic disease mitigation problems that are studied here , because very limited and heterogeneous control resources must be used in many zoonotic-disease control scenarios .'], ['Brucellosis is a zoonotic bacterium with several species that cause illness in livestock ( including cattle , small ruminants , pigs , camels , and bison , see e . g . [16]–[19] ) , wildlife ( including bison , elk , and caribou ) , and humans .', 'The disease in animals is chronic and impacts the reproductive system , with abortion , reduction in fertility , reduced milk yield , and abscess formation as typical signs ( that may be temporary or long-term ) .', 'Brucellosis may also be transmitted from these species to humans , in whom the disease is manifested in severe intermittent fever and extreme fatigue and malaise over a period of weeks or even months , sometimes progressing to a chronic disease with possibility of relapse and numerous complications ( including joint/bone problems , gastrointestinal problems , and abortion , among others ) .', 'Where the disease is prevalent , it may have significant societal and economic impact due to both reduced yield in livestock agriculture and loss of human life and productivity .', 'The most common strain of Brucella in cattle and various wildlife is B . abortus .', 'Transmission of B . abortus is primarily through contact with aborted fetuses or , in humans , ingestion of raw products from the livestock ( such as unpasteurized milk ) .', 'Pastoralists are often subject to both means of transmission , while a broader segment of the community in developing countries may be subject to infection from consumption of raw products , see e . g . [1] for details .', 'The developed model tracks brucellosis prevalence ( numbers of infectives ) in individual herds for multiple animal species and prevalence in human subpopulations ( divided by susceptibility ) .', 'Specifically , brucellosis infection is modeled in types of animals ( i . e . species , or possibly subspecies or breeds if transmission characteristics are different ) , labeled , which may include both livestock and wildlife .', 'For species , let us assume that herds or groups are present , labeled .', 'Because the disease is typically chronic in livestock , and dominantly impacts the reproductive system , we believe that considering a single infection class for each herd is sufficient for the initial controller design being pursued here .', 'Specifically , the number of infected individuals in herd of species at a time , denoted by for , , is tracked oer time .', 'The total number of individuals in the herd is assumed constant with the motivation that , over the time horizon of interest , economic and resource-limit determinants typically keep herd sizes relatively stable; the herd size is denoted by .', 'Additionally , the number of people infected with brucellosis is tracked in human sub-populations , labeled , that have different interaction characteristics with livestock .', 'Here , we first develop a predictive mathematical model for the dynamics of the infection counts and , in the nominal case without application of designable controls .', 'Infection-spread dynamics at the scale of herds or sub-populations are often represented using deterministic differential-equation models ( known as multi-group models ) in the mathematical epidemiology literature [6] , [14] , and we use and enhance this modeling paradigm here .', 'Given the above-described mechanisms of transmission , it is clear that both transmission between individuals within a herd and transmission among herds ( of one or several species ) whose members commingle is possible , and we model both means of transmission here .', '( We note that inter-herd transmission may be especially common for transhumance herds , or ones that share a confined space with other herds in a production system . )', 'Within the herd of species , the infection rate due to inter-herd interactions is modeled as proportional to the product of the infected population and the non-infected population , i . e ; this classical quadratic model is appropriate since the frequency of sexual contact and/or contact with infected birth material ( and hence the infection rate ) should roughly scale with the pairwise interactions between infectives and non-infected herd members .', 'Even in areas with high brucellosis prevalence , the infected population is typically relatively small ( 25% ) compared to the total population ( see e . g . [17] ) .', 'Thus , the approximation that the non-infected population is approximately equal to the ( constant ) total herd population is usually apt .', "Under these conditions , the rate of infection at time due to transmission within the herd can be modeled by the linear function , where is a breed-specific and herd-specific scaling constant that captures likelihood of spread through interaction ( and reflects , for instance , duration of the disease's survival in an aborted fetus , the prevalence of the bacteria in excretion , or the size of the pasture for grazing ) .", 'Such linear approximations for transmission have been routinely used in network models of spread , and are well-motivated for use in controller design [6] , [13] , [14] .', 'Here , the linear approximation was used for surveillance and control design , while the nonlinear population-dynamics models was used to verify designs and in identification of model parameters .', 'Next , the model captures transmission from other herds of the same species .', 'Specifically , consider transmission from a herd of species to the herd of species , where .', "For this pair , the transmission rate is governed by the uninfected population of herd and the infected population of herd , and is modulated by the extent of commingling of the two herds ( or , more specifically , interaction of herd 's individuals with herd through mixing of the herds or other means , such as purchase of an animal ) .", 'This extent of interaction is captured in the model using an interaction scaling parameter , where represents identical commingling as would happen within a single herd , and is typically much smaller than .', 'Using the same assumptions on populations that yield a linear model for within-herd tranmission ( from to ) , the inter-herd infection rate is modeled as .', 'Thus , the total rate of infection for herd due to transmission from other herds of the same breed is .', 'The rate of infection from herd of species to herd of species is modeled analogously with the intra-species transmission , but with allowance for varying infectivities .', 'Specifically , the linearized model for this infection rate is .', 'Thus , the total infection rate due to transmission from other species/breeds is .', 'The model also captures changes in infection counts in a herd due to 1 ) natural death or ( rarely ) remission , and 2 ) incorporation of infected animals from outside the modeled system ( e . g . , through purchase of the animals by a pastoralist ) .', 'The rate of decrease in infectives due to death/remission is well-modeled as proportional to the number of infectives in the herd .', 'Specifically , in herd of species , the rate at which infectives decrease through natural death is given by in the model , where is a species-dependent death/remission rate .', 'Secondly , the infection rate due to injection of infected animals from outside is represented as an input for each herd of breed .', '( These additions to a herd are not viewed as changing the size of the herds significantly , but rather reflect e . g . purchase of a few animals to replace losses . )', 'In the case where the linear model is in force , the following family of differential equations for nominal brucellosis transmission in the livestock/wildlife population is obtained , by summing the transmission rates to each herd and subtracting the natural death rate: ( 1 ) for and .', 'The above model is highly abstracted , in the sense that only one infection state is assumed for each species and the stochastics of transmission are ignored entirely .', 'The model dynamics are in general nonlinear ( and we can use the nonlinear approximations as needed ) , even though our focus has been on the linear approximation with the assumption that the infection fractions are relatively small .', 'This simplistic model for the dynamics is compelling in that it 1 ) allows systematic controller design and development of simple insights about resource allocation ( whereupon a detailed simulation model can be used to test the design ) and 2 ) exposes the role played by the network structure in spread and spread control .', 'A second core aspect of the nominal model is the representation of brucellosis transmission from livestock to the human population prior to control .', 'As with the animal model , infection of the human population is captured through representation of the infection rate at each time , thus yielding differential-equation models of transmission .', 'To roughly capture these infectivity characteristics in a way that permits control design , a linearized population-dynamics model is again used to describe the spread .', 'In particular , each subpopulation is assumed to have an infection rate that is a linear combination of the infective counts in various herds , i . e . the infection rate for human subpopulation at time is , where captures the rate of infection caused by herd of species .', 'In addition to infection from livestock , the number of infected individuals in each human subpopulation are modeled as declining due to death or remission at time , at a rate .', 'Combining these rates , the number of infected individuals in the human subpopulations are modeled by the following differential equations: ( 2 ) The nominal model for brucellosis transmission described above can be viewed as a network model .', 'In particular , viewing the herds and human subpopulations as components in a contact network , we see that there are interactions between pairs of these components if and only if commingling and transmission occur for that pair ( with the stength of the interaction reflected in the weight of associated coefficient in the differential equation ) .', 'To facilitate analysis and design , it is worthwhile to define a weighted and directed nominal spread graph or simply spread graph that captures the contact network structure .', 'In particular , the spread graph is defined to have vertices or nodes , representing each livestock herd and human subpopulation .', "An arrow or edge is drawn from one vertex to another , if and only if the herd/subpopulation corresponding to the first vertex directly impacts the infection rate in the herd/subpopulation corresponding to the second vertex ( i . e . , if the first herd's infection level is present on the right side of the differential equation for the second herd ) .", 'The weight of the edge is set equal the corresponding coefficient in the linearized differential equation , since this coefficient captures the strength of the interaction .', "This formulation of a graph includes self-loops , or edges from vertices back to themselves , whose weights are chosen in the same way as for other edges ( equal to the coefficient of the herd's infection level in its differential equation ) .", 'The self-loop weights will be negative , in the case that the rate of remission/death is larger than the spread rate in a herd .', 'The spread graph never has arrows leading out from a vertex representing a human subpopulation , and the self-loops for these vertices are always negatively weighted , since humans do not transmit the bacteria .', 'An illustration of a spread graph is given in Figure', '1 . In that the spread graph specifies the contact network ( i . e . , the transmission rates ) among modeled populations , we note that specifying the spread graph accurately for examples of interest is of critical importance .', 'Let us stress that , in general , three different approaches may be used to specify the spread graph: 1 ) the control-strategy planner may use intimate knowledge of an agricultural system to identify herd contacts and postulate transmission rates; 2 ) a formal system-identification methodology may be used to infer the spread graph; or 3 ) for large-scale networks , existing characterizations of typical network topologies ( for instance , “small-world topologies” wherein all subunits are within a few steps of each other in the graph despite relatively spare connectivity ) can be used to generate plausible spread graphs .', 'In the illustrative example presented in the results , we will motivate and describe the specification of the spread graph that we have used for this example .', 'Next , the nominal multi-group model for brucellosis transmission is enhanced to explicitly represent surveillance and control capabilities 1 ) within the animal population and 2 ) for transmission from animals to humans .', 'In the animal population , control of spread is achieved through several means , including 1 ) vaccination , 2 ) surveillance for and culling of diseased animals , 3 ) limitation of herd commingling ( through restriction of trade or movement of livestock ) , and 4 ) improvement in sanitation at farms ( e . g . , [18] ) .', 'Broadly , these various control capabilities can be viewed as impacting the dynamics of the model in two ways: 1 ) they alter the rate at which one herd/subpopulation causes brucellosis infection in another herd , or in other words change the model parameters ( equivalently , the edge weights in the nominal graph ) ; and 2 ) they cause removal of infected individuals at particular times , i . e . they serve to change the state variables and .', 'These changes can be captured as modifications and feedback control terms in Equations 1 and', '2 . The layered network model for zoonotic disease transmission that we have introduced above , using brucellosis as a case study , is promising as a tool for systematic design of mulitfaceted control capabilities .', 'Precisely , the formulation permits application of some new methodologies for network control theory , for the systematic design of limited control resources to achieve high performance ( low spread cost ) , or equivalently to reduce totaled resource and spread cost .', 'The approach is also promising in that the simple model structure can permit determination of model parameters ( parameterization ) from sparse historical data , and hence the approach is potentially applicable in the limited-data settings that are common in zoonotic disease spread .', 'In this section , we overview the network-control-theory methodologies for high-performance design and model parameterizaton .', 'We aim to present the methods in sufficient detail that the reader understands the concepts and essential methodologies underlying design/parameterization; to allow wide readership , we exclude technical justifications and algorithmic details , and refer the reader to specific results in the engineering literature for these .', 'Before describing the methodologies for control design and parameterization , let us stress that the modeling framework permits simple simulation and analysis of the spread dynamics , for a specified control policy .', 'In particular , we note that both the linear and nonlinear differential-equation models can be solved numerically using standard derivative-approximation methods , and can be implemented readily using e . g . the Matlab software .', 'The linearized model also readily permits analysis of the dynamics , including closed-form computation of steady-state and transient dynamics , and computation of features of the dynamics such as the basic reproductive number .', 'This analysis is based directly on the classical analysis of linear systems or linear differential equations; we kindly refer readers who are not familiar with the classical methodology to see [20] .'], ['The nominal spread graph , which illustrates the contact network prior to control , is shown in Figures 2 and 3 .', 'Simulations of spread among the cattle herds are shown for two different initial conditions , one with a single infective in a transhumance herd and the other with a single infective in a sedentary herd ( Figures 2 and 3 ) .', 'The basic reproductive number for the nominal model in the animal population is greater than , and as expected the infection becomes widespread for both initial conditions .', 'The infection spreads much more rapidly when it initiates in a transhumance herd .', 'Interestingly , even when the infection initiates in a sedentary herd , it eventually becomes more prevalent in the transhumance herds .', 'We note in these examples that we have initiated the infection in the largest sedentary and transhumance herds .', 'We did so because the larger herds display a faster initial growth of the infection , leading to a more rapid ( and easier to display ) spread in the network .', 'We stress that , qualitatively , the response characteristics would be similar if the infections were initiated in smaller herds , though the progression would be slower .', 'The model also shows that the infection rate in the human subpopulation that is responsible for animal husbandry grows rapidly in the early stages of the infection .', 'A couple remarks about the nominal model are worthwhile .', 'Remark 1 .', 'In the 20-herd example chosen above , we note that the graph topology of the contact network is one where half of the vertices have high degree , while the remaining vertices have low degree: the graph is generated to enforce a degree distribution , but chosen randomly within this constraint; the particular transmission rates used in the example are obtained through identification of the brucellosis spread model .', 'Such random graphs with enforced low- and high- degree vertices have some properties in common with the common small-world graphs when they are of sufficient size , and in this sense our results for the example may be indicative of results when the topology is a small world .', 'We stress , however , that our analysis methods ( and subequent control design and identification methods ) can be applied regardless of the graph topology , and that the specific topology that we have chosen is guided by our understanding of the agricultural practices governing brucellosis spread rather than by the typical model classes considered in the complex-systems literature .', 'Remark 2: In the above example , we have excluded transmission to and from wildlife , because of the difficulty in parameterizing wildlife-related transmission rates .', 'Model simulation and analysis when transmission to wildlife is considered is straightforward .', 'For instance , we have completed simulations in which an identical rate of transmission between each herd and wildlife is assumed: as expected , disease prevalence increases with increasing transmission rate to and from the wildlife reservoir .', 'In practice , we conjecture that the transmission rates between each herd and the wildlife reservoir are better modeled as random quantities , reflecting variability in the extent of contact with wildlife .', 'We leave further development to future work .', 'Several strategies for vaccination , namely ones that are targeted to tranhumance herds vs . ones that distribute resources between tranhumance and sedentary herds , are compared in the 20-herd example .', 'In particular , herds are modeled as being vaccinated at a certain frequency , with the cost needed for each vaccination of a herd assumed identical in this illustrative example .', '( The relative cost of vaccinating sedentary and transhumance herds may sometimes be rather varied in practice: in some settings , transhumance herds may be incredibly difficult to reach for vaccination , while in other cases medical personnel may be able to take advantage of their mobility by placing vaccination capabilities at a location frequented by these herds . We take the simplest assumption of identical cost for ease in illustration , but the design can be achieved for other cost structures also . )', 'Three strategies with identical total resource cost are compared: one that vaccinates only the transhumance herds , one that vaccinates sedentary and transhumance herds , and one that vaccinates only the sedentary herds .', 'For the three vaccination strategies , the basic reproductive ratio , which can be calculated from the spectrum of the state matrix of the linearized model dynamics ( see [6] , [14] for details ) , is compared .', 'The results are shown in Figure 4 .', 'When resource limits are low , vaccination of transhumance herds can reduce the basic reproductive number below while a uniform vaccination strategy or a sedentary-herd vaccination strategy cannot .', 'When more resources become available , uniform vaccination becomes comparable and eventually preferable to only transhumance-herd vaccination ( and reduces to ) .', 'However persistent infections still tend to be common in the tranhumance herds .', 'It is hypothesized that improved surveillance techniques that permit fast and cheap decentralized surveillance/culling could significantly improve brucellosis control .', 'The model permits evaluation of the benefits of faster surveillance/culling .', 'Here , a uniform surveillance/culling policy at all herds is considered for the -herd example .', 'Specifically , the dependence of an infection cost ( specifically , the infected animal population integrated over time ) on the surveillance/culling rate is identified .', 'This dependence , shown in Figure 5 , indicates the improvement in spread mitigation due to faster surveillance/culling .', 'Using this type of characterization , a practitioner can evaluate whether the additional cost to design new surveillance/culling techniques is worth the improvement in spread cost due to these advances .', 'Here , we consider a homogeneous surveillance/culling procedure for all herds , and calculate the integrated infection size ( the number of infected animals integrated over the duration of the infection ) for the 20-herd network , for a random initial condition .', 'In this example , a culling rate of at least 0 . 43 ( 43% of the infected population per annum ) is needed to make less than ; however , higher culling rates beyond this threshold significantly reduce the total infection size .', 'The modeling methodology that we have introduced permits systematic optimization of control resources , according to the methods outlined above .', 'For illustration , we have found the optimal allocation of vaccination resources to minimize the basic reproductive number in the illustrative example , as a function of the level of available resources .', 'The optimal basic reproductive number , and the fraction of the resources that are allocated to the transhumance herds , are plotted in Figure 6 .', 'The impact of the vaccination policy on the rate of infection in human pastoralists is also shown ( Figure 7 ) .', 'As a comparison with the optimal vaccination strategies ( Figure 6 ) , the performance of an optimal surveillance and culling strategy ( in terms of the achieved basic reproductive number ) is also shown ( Figure 8 ) .', 'Finally , concurrent design of surveillance/vaccination capabilities and pasteurization to prevent transmission to humans is considered in the -herd network .', 'In this simple example , the costs of vaccinating each herd and of pasteurizing the milk from each herd are all assumed to be identical , and the optimal design ( with respect to a total infection size measure ) is examined for different human vs . animal infection costs .', 'The results are shown in Figure 9 .', 'The techniques described above for identification of the bovine brucellosis model from snapshot and time-course described were applied .', 'The results of the identification are displayed in Figures 10 and Figure 11 .', 'The identified parameters have been used to specify nominal intra-herd and inter-herd transmission rates in the illustrative example .'], ['The network control methods allow a comprehensive study of the brucellosis controller design problem , and more generally of zooonotic-disease control .', 'Below is a list of several aspects of the control design task that can be addressed using these methods , as well as a few of the key insights obtained through the design .', 'These insights are envisioned as informing policy decision-making .', "1 ) Optimal or high-performance sub-divisions of control resources among the animal herds can be determined , based on the spread graph's structure .", 'When resource allocation costs and infection costs due to prevalence in a herd are relatively homogeneous , then high-performance designs tend to equalize the spread-impacts of the herds , to within the extent allowed by the constraints on resources and on the control .', "Thus , limited resources ( whether for vaccination , surveillance/culling , or other purposes ) should be allocated to herds with high spread impact ( sum of outgoing edge weights from that herd's vertex on the graph ) , until the spread impacts are equalized .", 'If further resources are available , they should be equally distributed among the herds , if possible .', 'When constraints prevent allocation of resources ( or further resources ) to some herds , the design becomes somewhat more intricate: some herds must be alloc
['Introduction', 'Methods', 'Results', 'Discussion']
['Developing control policies for zoonotic diseases is challenging , both because of the complex spread dynamics exhibited by these diseases , and because of the need for implementing complex multi-species surveillance and control efforts using limited resources .', 'Mathematical models , and in particular network models , of disease spread are promising as tools for control-policy design , because they can provide comprehensive quantitative representations of disease transmission .', 'A layered dynamical network model for the transmission and control of zoonotic diseases is introduced as a tool for analyzing disease spread and designing cost-effective surveillance and control .', 'The model development is achieved using brucellosis transmission among wildlife , cattle herds , and human sub-populations in an agricultural system as a case study .', 'Precisely , a model that tracks infection counts in interacting animal herds of multiple species ( e . g . , cattle herds and groups of wildlife for brucellosis ) and in human subpopulations is introduced .', 'The model is then abstracted to a form that permits comprehensive targeted design of multiple control capabilities as well as model identification from data .', 'Next , techniques are developed for such quantitative design of control policies ( that are directed to both the animal and human populations ) , and for model identification from snapshot and time-course data , by drawing on recent results in the network control community .', 'The modeling approach is shown to provide quantitative insight into comprehensive control policies for zoonotic diseases , and in turn to permit policy design for mitigation of these diseases .', 'For the brucellosis-transmission example in particular , numerous insights are obtained regarding the optimal distribution of resources among available control capabilities ( e . g . , vaccination , surveillance and culling , pasteurization of milk ) and points in the spread network ( e . g . , transhumance vs . sedentary herds ) .', 'In addition , a preliminary identification of the network model for brucellosis is achieved using historical data , and the robustness of the obtained model is demonstrated .', 'As a whole , our results indicate that network modeling can aid in designing control policies for zoonotic diseases .']
['Zoonotic diseases ( ones that infect both animals and humans ) exact a significant economic and human cost , especially in developing economies .', 'Developing effective policies for mitigating zoonotic infections is often challenging , both because of the complexity of their spread and because very limited resources must be allocated among a range of control options .', 'It is increasingly becoming clear that mathematical modeling , and in particular network modeling , of disease spread can aid in analyzing and mitigating these spreads .', 'Here , we develop a network model for the spread and control of a zoonotic infection , focusing particularly on a case study of brucellosis transmission and control among wildlife , cattle herds , and human subpopulations in an agricultural community .', 'After motivating and formulating the model , we introduce tools for', '1 ) parameterization of the model from time-course and snapshot data ,', '2 ) simulation and analysis of the model , and', '3 ) optimal design of control policies using the model .', 'The study shows that the network model can inform design of heterogeneous control policies that mitigate zoonotic disease spread with limited resources .']
['medicine', 'control engineering', 'computer science', 'veterinary diseases', 'public health and epidemiology', 'computer modeling', 'veterinary epidemiology', 'epidemiology', 'animal management', 'veterinary science', 'agriculture']