Numerous studies have demonstrated that exposure to live poultry or live poultry markets is the significant risk factor for human infection with avian influenza A(H7N9). However, the specific live poultry markets that are major infection sources for A(H7N9) human cases have not been explored in detail. In this study, we extract data associated with poultry farms, live poultry markets and farmers’ markets from Baidu Map using the JavaScript language and then construct the live poultry transport network. From this, we establish our A(H7N9) transmission model over the network based upon probabilistic discrete-time Markov chain. On the basis of the obtained network and model, we propose spatiotemporal backward detection and forward transmission algorithms to detect the most likely infection sources and to compute the first arrival times of the infection sources. Our simulations use these algorithms to identify the specific locations of the infection sources, the first arrival times of the infection sources and the most likely transmission map of the A(H7N9) virus along the live poultry transport network. The results reveal that, in addition to the hazards posed by the live poultry markets, backyard poultry also contributed to A(H7N9) human infections; this risk source was significant especially in the newly affected provinces, in the fifth wave of infection. In particular, by analyzing the temperature characteristics at a given location when the infection source arrived, we find that the risk of human infection with the influenza A(H7N9) virus was high under 9 ◦C∼19◦C; moderate under 0◦C∼9 ◦C or 19◦C∼25◦C; and low for temperatures < 0 ◦C or > 25◦C. Our results suggest that strengthening the supervision of the live poultry market system and immunizing poultry at both live poultry markets and the backyard poultry operations under the high risk temperature band of 9 ◦C∼19◦C, will be able to significantly contribute to the control of avian influenza A(H7N9) in the future.

Introduction

The novel avian influenza A(H7N9) virus emerged in 2013. It is a bird flu strain of the influenza virus A (avian influenza virus or bird flu virus) [1]. The avian influenza A(H7N9) virus is only transmitted between poultry or from poultry to human. Human can be infected through direct exposure to poultry, poultry secretions or excreta, inhalation of viral aerosols, and exposure to environments contaminated with the virus [2]–[4]. Human cases of A(H7N9) infection have occurred since 2013, during the annual winter-spring epidemics in mainland China [5], [6]. After peaking in 2013-2014, the human infection cohort in subsequent epidemics was generally smaller [7], but it sharply increased in the fifth epidemic wave in December 2016 [8]. This fifth epidemic wave (lasting from October 1st, 2016, to September 31st, 2017) was the most significant up until that point; 746 human cases were reported across 27 provinces in mainland China. The A(H7N9) virus strains circulating among poultry had been classified as low pathogenicity avian influenza (LPAI) in the previous four epidemic waves in China [9], but evolved to be highly pathogenic in poultry in the fifth epidemic wave [10]. The earlier start date, larger epidemic size, wider epidemic range and higher pathogenicity in the fifth epidemic wave A(H7N9) prompted panic and aroused public concern. Most of the confirmed A(H7N9) cases in human had an etiology involving a history of recent exposure to live poultry or potentially contaminated environments, especially the live poultry markets, where live poultry is sold [11], [12].

1- Introduction

2- Definitions and notations

3- Review of some existing similarity measures between fuzzy numbers and its limitations

4- Proposed similarity measure between GFNs with different left heights and right heights

5- Comparative analysis

6- Application of the proposed method in risk analysis

7- Conclusions

References

Abstract

Similarity measure of fuzzy numbers plays an important role in the risk analysis problem. Generally, it is tool, which gives lingustic term to the risk obtained. In recent times, a vast numbers of literature are evident on application of similarity measure in risk analysis. It has been observed that the existing similarity measure on fuzzy numbers have numerous drawbacks and limitations. Hence, a robust method of similarity measure is necessary. With this point of view, a new method to measure the degree of similarity between fuzzy numbers has been proposed. The method has been discussed based on the concept of value, ambiguity, radius of gyration point, geometric distance and the height of fuzzy numbers. The concept of value and ambiguity have never been used in similarity measure of fuzzy numbers. However, the inclusion of these concepts value and ambiguity contributed in many ways in overcoming the limitations and drawbacks of the existing similarity measures. The out-performance of the proposed method is illustrated by comparing with existing methods of similarity measure. Further the proposed method is effectively applied in risk analysis of poultry farming.

Introduction

Fuzzy risk analysis has become very popular in recent times as the knowledge of expressing imprecise quantity in terms of fuzzy numbers has emerged. Most of the time similarity measure between fuzzy numbers is used in the risk analysis problem and other decision making problem. The similarity measures are defined on the different characteristic of the fuzzy number such as geometric distance, center of gravity (COG), area, radius of gyration (ROG) etc. Further, these measures are being generalized for use in different types of fuzzy numbers. It has been observed that the existing similarity measures on fuzzy numbers bear various limitations and drawbacks. A review of some of the existing methods to measure the degree of similarity reveals various limitations and drawbacks. Chen (1996) defined a similarity measure based on the geometric distance. This definition does not carry the information about the shape of the fuzzy numbers such as triangular, trapezoidal, etc. Hence, in many circumstances this method fails to give a proper degree of similarity between fuzzy numbers. Hsieh and Chen (1999) proposed a similarity measure between two fuzzy numbers using graded mean integration representation distance. This method has no contribution from heights and shapes of the fuzzy numbers. Hence, the method is confined to normal fuzzy numbers. As like Hsieh and Chen’s method Lee’s (2002) method is just confined to normal fuzzy numbers. As such, it is not going to give correct similarity between fuzzy numbers having different heights and shapes. So far, the information about the heights is missing in the similarity measures. Hence, Chen and Chen (2001) developed a similarity measure for generalized fuzzy number (GFN) using the concept of the COG. Although this method seems to outperform in many situations, yet drawbacks are obtained in some situations as discussed in the Section 3. Replacing Chen and Chen’s COG by ROG, Yong, Wenkang, Feng, and Qi (2004) proposed a new similarity measure and applied in pattern recognition problems. The method seems very promising. However, it fails to give proper similarity between crisp-valued fuzzy numbers. Wei and Chen (2009) proposed a measure based on the geometric distance and the perimeter of the fuzzy numbers. However, the method fails to give proper similarity between fuzzy numbers depicting similar shape located at different positions. Xu, Shang, Qian, and Shu (2010) again used the COG and the geometric distance in measuring the degree of similarity between GFNs. Although the method is based on GFNs yet it fails to measure similarity between fuzzy numbers depicting similar shape with different heights. Hejazi, Doostparast, and Hosseini (2011) used the concept of geometric distance, perimeter, area and height to discuss the degree of similarity. However, the drawbacks are pointed out by Patra and Mondal (2015).

Providing care for groups of animals is a major part of practicing zoologic medicine. Herd health is key to the mindset of a zoo clinician no matter the species encountered, be it avian or artiodactylid. In addition to the classic examples of group treatment involving chemotherapeutics (discussed in detail later), zoo clinicians also practice herd health by preventing disease from entering the collection. Before traveling to a new institution, most animals undergo a preshipment examination, which serves as a screening tool for common infectious diseases specific to that taxa, and provides a snapshot of that individual’s health. Diagnostics commonly included in a preshipment examination are a complete blood count, serum or plasma biochemistry, imaging, and fecal examination. On arrival to a new institution, most animals undergo a quarantine period, often 30 to 90 days, in addition to another thorough examination. All of these precautionary measures are vital to ensure that infectious disease does not enter an institution, and also provide the opportunity for targeted therapy if needed, before the animal is placed within its new social group. It is highly recommended that all animals that die within a zoologic setting receive a thorough gross necropsy with histopathology to try and determine the cause of death. Then, if an infectious cause is diagnosed, therapy for the remaining group of animals is based on the pathology findings. Another way that zoo clinicians can try to limit the need for group treatment is to have a working knowledge of which taxa can be safely housed together. In addition to such factors as size and potential for trauma, knowledge of how certain infectious diseases interact with various species can prevent future outbreaks. For example, Entamoeba invadens is transmitted from clinically healthy herbivorous tortoises to snakes when they are housed together, causing the snakes to develop severe ulcerative colitis and hepatitis.1 If a disease outbreak does occur, practicing vigilant biosecurity to try and limit transmission is key to decreasing the number of animals affected and needing treatment. Depending on the etiologic agent footbaths, isolation, and appropriate personal protective equipment may be used.2 When treatment is needed in a zoologic setting it presents unique challenges. One obstacle commonly encountered is that few pharmacokinetic studies have been performed in the species commonly found in zoos, so doses are often extrapolated from their closest domestic relative. Although extrapolation from domestics is done easily for some taxa, such as exotic canids, felids, or equids, there are species with no domestic counterpart, such as marsupials or invertebrates. Several different types of interspecies scaling have been described in the literature, with allometric scaling considered the most accurate.3 However, there are limiting factors to consider when using allometric scaling, such as the route of elimination and the extent of metabolism of the selected therapeutic agent.3 An additional challenge is that often accurate body weights cannot be obtained, so estimated weights are used, which can increase the risk of underdosing or overdosing an animal.4 Group treatment is not common for some taxa, such as large carnivores, and individual treatment is advised when possible. Once a dosage has been selected and a weight obtained or estimated, the next question is how to administer the drug to the animal. Treatment options are heavily dependent on the species, and are covered in detail in the following sections. Group treatment is not standard for all taxa, so only the most common species are discussed.

The global urbanization process has led to a rapid transformation of various urban and suburban habitats with profound consequences for biodiversity (e.g. McKinney 2006; Seto et al. 2012). Improving the conditions for biodiversity in cities has been suggested to contribute to quality of life for city dwellers (e.g. Tzoulas et al. 2007; Standish et al. 2012). For instance, human well-being in cities has been attributed to, among other factors, access to green space with variety in the form of species-rich habitats (e.g. Fuller et al. 2007; Dallimer et al. 2012). One important aspect of the presence of various organisms in urban areas is the opportunity for people to experience plants and animals for recreational purposes. This can be viewed as part of the ecosystem services in cities, i.e. the various benefits that humans receive from ecosystems including urban ones (MEA 2005; Clark et al. 2014). For many urban inhabitants, the everyday experience of biodiversity is gained by visiting a nearby green space in the city.However, there are still a number of less well-known links between people and biodiversity in urban green space. A focal question is how green space is perceived. We focus here on (1) the possible Bmismatch^ between variation in urban biodiversity and how it is perceived (e.g. Dallimer et al. 2012); (2) the importance of environment-related attitudes of different individuals for perception of green space (e.g. Lin et al. 2014); (3) how the natural sounds in urban green space are perceived in relation to biodiversity and environmentrelated attitudes (e.g. Viollon et al. 2002; Irvine et al. 2009). These approaches were employed because our previous studies have shown that environment-related attitudes and natural sounds influence perception (Knez and Thorsson 2006, 2008; Hedblom et al. 2014). Here we investigate the effects of, and interactions between, these factors regarding perception of urban green space. Below, we describe the concerns that are related to the three approaches. First, the relationship between actual and perceived biodiversity may not be so straightforward as might be expected (e.g. Fuller et al. 2007). Several studies have recently focused on this problem (Dallimer et al. 2012; Shwartz et al. 2014; Pett et al. 2016). For instance, in a study in England, it was shown that the well-being of visitors to green space was positively related to the perceived species richness of plants, birds and butterflies. But no consistent pattern was found between actual, measured species richness and the well-being of participants in the study (Dallimer et al. 2012). In other studies, the vegetation has been in focus because it is usually a major part of the perceived urban biodiversity. When flower diversity was experimentally increased in small public gardens in Paris, the visitors did not perceive any change in diversity before and after the manipulation although the participants expressed a preference for species richness (Shwartz et al. 2014).