Probabilistic Supply Chain Risk Model for Food Safety1


a School of Public Heath (Division of Environmental Health Sciences) and College of Science and Engineering, University of Minnesota – Twin-Cities, Minneapolis, MN, USA. E-mail: b Department of Environmental and Global Health, and Emerging Pathogens Institute, University of Florida, Gainesville, FL, USA, E-mail:

Abstract — Food safety is a complex issue for the worldwide population. Over the last decade foodborne outbreaks have shown an increasing trend. Foodborne outbreaks in the USA caused in 2010 a cost of $ 152 billion related to 325,000 hospitalized persons and 5000. Scalable models that address the need of integrating epidemiological, social, and trade information in an operation research setting are in strong demand to reduce the US and global public health risk. Here we propose a model for the assessment of the potential health risk of food commodities based on the food supply chain (FSC) as a subset of the international agro-food trade network. The model integrates concepts of network science in the supply chain and risk factors related to the food life-cycle that occurs along the FSC. We consider the food-pathogen risk from the production to the distribution, screening and manufacturing flaw risks, transportation and intermediary country risks, country and manufacturer risks. The number of connected countries, the betweenness centrality of the exporting countries, and the average path length are the supply network variables considered. Considering the safety of each country and the network variables we introduce a global safety index (GSI) for characterizing the riskiness of each country based on local and FSC variables. The potential health risk is characterized by a multimodal distribution and a ranking of food-pathogen-country triples reveals the unsafest paths of the FSC. Global sensitivity and uncertainty analyses show that the network variables are driving the potential health risk, thus they are crucial for public health risk management. The intermediary country risk, the food-pathogen health risk, and the company reliability are the second most important factors for the potential health risk. Policies that act on both the supply chain variables and the safety index by means of the GSI reduce of 44 % the average health risk. This reduction is much larger than the reduction of policies focused on individual risk factors of the food life-cycle. Complex food, composed by multiple ingredients, are among the riskiest foods and their risk is driven by the FSC complexity. Current management practices are focused on intervention after local outbreak cases and food-pathogen relationships with little attention on prior global FSC interventions. The model can identify critical pathways in terms of safety of food, thus guiding surveillance. The FSC model here presented is scalable to any level of the global food system and offers a novel perspective in which the global public health is conceived, monitored and regulated.

Keywords — food safety, food supply chain, risk, pathogens, network, trade, public health.

1  Introduction

Table 1: Variables of the Food Supply Chain (FSC) model.
VariablesDescriptionDistribution and Range
ΦtTransportation risk factorsG (P: 0.2; Ra.: 0.4; I: 0.6; R: 0.7; S: 0.8; ±0.02)
ΦmIntermediate country risk factorG (DI ±0.5)
ΦcCompany risk factorU (MEAN ±0.5)
ΦhFood-pathogen risk factorG (MEAN ±0.5)
ΦnFood risk factor of the producing countryG (TI ±0.5)
ΦmfManufacturing flaw risk factorU (TI ±0.5)
ΦsfScreening flaw risk factorU (DI ±0.5)
LPath lenthExp./Power-law
bBetweenness centralityExp.
FFood importationExp.

1.1  Food safety, foodborne diseases, and potential health risk

Food production, “from farm to fork”, has become a globalized, complicated process to handle that is largely intertwined with other major problems such as food security, water availability and use, and the global economy. The World Economic Forum lists food-related issues as one of the most critical for the worldwide population. The food supply chain (FSC) for a finished product can incorporate multiple manufacturers and suppliers from around the world. Potential hazards to health may now come from all food commodities of the food supply

1.2  Previous approaches and challenges

One of the major issues in food safety is the lack of comprehensive studies that consider the multiplicity of factors related to food safety simultaneously. Previous studies and regulations have been focused on the characterization of microbiological, chemical, and physical safety of food processing separately. In a global risk perspective all risks and their interactions need to be considered together.

1.3  Proposed supply chain approach

In this paper we propose for the first time a supply chain based model for food safety. Specifically, we assess the current total risk considering all food commodities imported in the USA from the primary production to the port of entry. The choice of the USA is to answer the needs of the Food Modernization Act but also to show its substantial importance as a model that can quantitatively be implemented and adopted worldwide for the safety of the consumed food.

2  Methods

2.1  Risk assessment

The IAFTN is defined as a graph (V,F)t, in which V = vij represents the adjacency matrix where vij = 1 if i is connected to j, otherwise vij = 0, and F = fij is a directed weight matrix, in which each of its elements describes the food trade among countries. The subscript t represents an index indicating the network constructed in the time domain. For the IAFTN the trade can have two directions, thus V and F can be related to importations or exportations only. However, the supply chain of each country that is a subnetwork of the IAFTN is a direct network that considers only the importations. All the risk factors along the supply chain (Table 1) can be considered together to calculate the potential health risk, that is the risk at the port of entry of the country considered. This potential health risk considering all food commodity risks of all possible combinations of countries at any stage of the FSC is calculated. Further details and calculations are explained in (Convertino and Song, 2013).

2.2  Network variables

Here we define the FSC network variables used in the study. In this particular study we focus on the USA but all the network variables are also needed to calculated for all the countries in the US FSC. The supply chain length (or path length), L, is the length traveled by a selected food commodity on average. The node in-degree, kin, is defined as the number of incoming links to a node. The edge weight (or link weight) of the directed link (i,j) is defined as wji = −ln(Fij/Fmax) , where Fmax = maxijFij is the largest flux in the network. The betweenness centrality is a measure that rates the importance of the position of a node or an edge in the network with respect to transport through the whole network.

2.3  Safety indices

We introduce the Safety Index as the ratio of the Detector and Transgressor Indices (DI and TI, respectively). Thus, the safety index is SI = DI/TI. Because of the evidence calming from the potential health risk calculations based on the supply chain model the Global Safety Index is introduced as GSI = SI/L b kin, where L, b, and kin are the supply chain path length, the betweenness centrality, and the in-degree of each country respectively. Table 1: Variables of the Food Supply Chain (FSC) model. The risk factors and the FSC variables are evidenced in white and grey, respectively. Φt is estimated from (Ackerley et al., 2010) (P, Ra., I, R, S, and W stand for plane, railroad, intermodal, railway, storage, and water transportation), Φm is the Detector Index (DI) from data of (RASFF, 2013) implemented in (FAN, 2013) (Nepusz et al., 2009), Φc is estimated from (FPR, 2013) based on the sales of each food company, Φh is from the risk assessment of (Batz et al., 2011) (see Table “ES-2”) and (Batz et al., 2012), Φn is the Transgressor Index (TI) (Nepusz et al., 2009; FAN, 2013; RASFF, 2013), Φmf and Φsf are distributions similar like the TI and the DI Index because of the absence of surveillance data. Here, we introduce the risk factors for both the country where the food is produced, the producing company, and the systematic or accidental risks of manufacturing and screening. G stands for Gaussian, and U for uniform. The food-pathogen pair risk was assessed by Batz et al., (2011), considering infectious disease prevalence in the USA.

Figure 1: Agro-Food International Trade Network and Supply Chain factors.

In figure 1 the superposition of all supply chains assigns a value, the salience (i.e., the sum of all L divided by the number of connections), to each link in the Agro-Food International Trade Network (AFITN). The salience permits an intuitive definition of a network’s backbone as a network which incorporates the collection of links that accumulate at a normalized edge weight ∼ 1. Salience values are shown on the right with link color: red is high salience and grey is low. Edge weights is capturing the intensity of food trade between two countries at the two endpoints of the edge. Bottom: food supply chain (FSC) scheme and FSC variables (Table 1). The edge width is proportional to the trade and the size of the node is proportional the Safety Index (SI) (Table 1). The potential health risk is calculated at the end of the FSC. The trade is typically reported only from the raw ingredient countries (1 to 3), or the last intermediate country (8), to the importing country (country 9) without information about the intermediate countries along the supply chain (red dotted line). However, this is not enough to decrease foodborne risks for the public health.

In figure 2 the combinations food-pathogen-country that determine the highest values of the risk in each range shown in the squares is reported. The probability distribution function is generated by running the FSC model with the variables in Table 1 for any food commodity and country. The variability of the distribution (shaded red area) is calculated by the uncertainty analysis using the distribution of variables for the FSC in Table 1.

Figure 2: Distribution of the potential health risk for the USA, and potential health risk versus supply chain variables.

3  Results and discussion

The food safety in any country is related to the country supply chain that is a directed subnetwork of the International Agro-Food Trade Network (IAFTN) depicted in Figure 1. The potential health risk is reported in Figure 2. This system health risk for the USA considers any food commodity, producing, processing, and distribution countries, food-pathogen pair, transportation, and company risk. The potential health risk for each food category is reported in Figure S6 in which the variability depends on all variables with the exception of all other food commodities. Hence, these risks are calculated by only considering the risk values of each food commodity for their food category. The variability of the distribution in Figure 2 is assed by global sensitivity and uncertainty analysis considering the distributions in Table 1. Monte Carlo filtering allows to assess the combination of food-pathogen-country that contribute the most to selected total risk value ranges. In Figure 2 we report these food-pathogen-country triples for some risk ranges, where the country can be the producing, processing, or distributing country. Thus, we consider each country in a global picture for the whole life cycle of food in terms of food- pathogen raking according to the defined risk value distributions, the findings are mostly in agreement with the ranking of (Batz et al., 2012).

4  Added value to the One Health approach

By considering the whole supply chain, its topologic features and determinant factors, we are able to assess multimodal probability distribution functions of the health risk that allow to (i) explore the whole range of potential public health risks; and (ii) to detect the source, path, food-pathogen-country, or other variables and combination of variables responsible for certain risk values. Hence, high health risk outcomes can be avoided by proper management strategies that act on the controlling variables. The results underlines the importance of the network, the validity of the GSI as a measure of risk of countries, but also the importance of a risk assessment based on both risk factors of the food life-cycle and supply chain variables.

5  Conclusions

Food safety is a complex problem related to the complex food system, from food security, safety to trade and quality, that yet requires a complex system science approach to be dis- entangled and managed (35). This is because of the multiplicity of the involved interacting factors (stakeholders, food commodities, and environmental factors) that determine multiples risks for food which has major implications for health and economies of the population worldwide. Here we present a model that for the first time integrates all known risk factors of the complex food system, from the production to the final distribution, considering the supply chain of food commodities along the network on which these factors propagate. We provide a probabilistic characterization of the risk and a ranking of food-pathogen-country triples. The supply chain connects scales and actors of the food safety problem, from the small scale of the food-pathogen pairs to the country scale, and all countries together in the life-cycle of food. Data of trade, country safety, and complex network variables have been used unitarily to characterize the potential public health risk for the USA at the port of entry.

We find that the most important factors of food safety are supply chain network variables regardless of the food commodity and countries considered. Specifically, the length, the importance of each country for the food trade, and the number of connected countries determine the number and level of risks related to food-pathogen, transportation, and manufacturing/screening combinations that ultimately affect the total risk. Thus, we introduce the Global Safety Index (GSI) that includes both safety index and network topology variables for characterizing the riskiness of countries. The GSI that is inversely proportional to the potential health risk is useful to characterize the safety of each country; however, the risk calculation is irreplaceable for the precise identification and prediction of the riskiest pathways of contamination of all food commodities or of some selected commodities. Moreover it is necessary to know how a risk is transferred from one country to another because the only knowledge of the “weak nodes” - in terms of food safety - is not enough especially in dynamically changing systems as the food system. Because of the importance of network topological variables we make scenarios of the potential health risk for different FSC topologies in which each topology has a complexity index.

By considering the FSC, there is a strong need to strengthen surveillance systems to critical nodes and links for the characterization of risk factors related to foodborne diseases. The identification of critical pathways for continuous surveillance can be informed by the presented model and surveillance data can be used by the model for planning, implementing and evaluating public health policies. The model is applicable to any scale, from towns to cities, country, and/or to the worldwide scale simultaneously to assess the health risk of population and to evaluate global management strategies that diminish the systemic health risk. This a large difference with respect to local single-risk management strategies evaluated in the past in literature and in practice. At the moment, there is probably too much incertitude and uncertainty about the food system. Nonetheless, it is certain that food safety should be seen as an highly dynamical process in which the prediction and detection of food safety alerts can occur in real-time with the availability of data, technological development used in the FSC, and the development of quantitative model using these data.


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Convertino,, M. and Liang, S.2014): Probabilistic Supply Chain Risk Model for Food Safety. In: Planet@Risk, 2(3), Special Issue on One Health (Part I/II): 191-195, Davos: Global Risk Forum GRF Davos.

This article is based on a presentation given during the 2nd GRF Davos One Health Summit 2013, held 17-20 November 2013 in Davos, Switzerland (

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