The world-wide waste web

Countries globally trade with tons of waste materials every year, some of which are highly hazardous. This trade admits a network representation of the world-wide waste web, with countries as vertices and flows as directed weighted edges. Here we investigate the main properties of this network by tracking 108 categories of wastes interchanged in the period 2001–2019. Although, most of the hazardous waste was traded between developed nations, a disproportionate asymmetry existed in the flow from developed to developing countries. Using a dynamical model, we simulate how waste stress propagates through the network and affects the countries. We identify 28 countries with low Environmental Performance Index that are at high risk of waste congestion. Therefore, they are at threat of improper handling and disposal of hazardous waste. We find evidence of pollution by heavy metals, by volatile organic compounds and/or by persistent organic pollutants, which are used as chemical fingerprints, due to the improper handling of waste in several of these countries.


Supplementary information guide
• Degree distributions of W4 networks.
• Chemical fingerprints common in hazardous waste.
• Centrality of countries in the W4 networks.
• Waste categories in types IV-VII. PEIWS analysis of wastes types IV-VII.

Degree distributions of W4 networks
For each of the type I-III we calculated the in-and out-strengths (weighted degrees) of its nodes and tested 17 probability distribution functions: beta, Birnbaum-Saunders, exponential, extreme value, gamma, generalized extreme value, generalized Pareto, inverse Gaussian, logistic, log-logistic, lognormal, Nakagami, normal, Rayleigh, Rician, t-location-scale, and Weibull. The goodness of fit is tested by calculating the following parameters: negative of the log likelihood (NlogL), Bayesian information criterion (BIC), Akaike information criterion (AIC), and AIC with a correction for finite sample sizes (AICc). The results are as follows.

Chemical fingerprints common in hazardous waste
It has been argued that all chemical substances which are outside their usual environments or at concentrations above normal represent a contaminant and that they become pollutants when accumulations are sufficient to affect the environment or living organisms. 1 The sources of these chemicals may be very diverse, but some of the top contaminants emerge from waste. These are the cases of heavy metals, such as arsenic, lead, mercury, hexavalent chromium, and cadmium; volatile organic compounds like vinylchloride, benzene, hexachlorobutadiene or persistent organic pollutants like polycyclic aromatic compounds, polychlorinated biphenyls and dioxins. 1 The distribution of contaminants across the world is very unequal with a bigger impact on low and middle-income countries. 2 In these countries there are serious problems with the disposal of waste, which is poorly managed, regulated or controlled, 2 and obsolete techniques are applied for their processing, which together with the lack of governmental infrastructure makes the situation critical. 2 The substantial inform "Chemical Pollution in Low and Middle-Income Countries" 2 has identified many of the problems emerging in these countries due to the chemical pollution in spite of the many internationally existing legislation, such as the Stockholm, Basel, and Rotterdam Conventions, and the Strategic Approach to International Chemicals Management (SAICM). Generally, the term "hazardous" waste (HW) is used to define waste with potential threats to public health 3 and the environment. It includes waste electrical and electronic equipment, commonly designated as e-waste, which has become the fastest-growing component of the solid-waste streams in the world. 4 E-waste disposal and its informal management generates highly toxic heavy metals, brominated flame retardants, non-dioxin-like polychlorinated biphenyls (PCB), polycyclic aromatic hydrocarbons (PAH), polychlorinated dibenzo-pdioxins (PCDD), polychlorinated dibenzofurans (PBDF) and dioxin-like polychlorinated biphenyls (DL-PCB). These compounds are endocrine disrupters, and most are neuro-and immune-toxic as well. Another important source of chemical contamination is the clinical and medical waste. 5-7 Some attention has been given to the cases of infection transmission due to the inappropriate disposal and handling of this type of waste, 5-7 but less is known about the chemical traces left by medical waste on the environment and human populations. Another growing source of chemical contaminants is municipal solid waste, which tripled from 1965 to 2015. 8 Waste problems in developing countries is aggravated by the transboundary trade of HW, which increases their burden of certain kinds of waste in those countries. 9-13 The problem should be analyzed from a wide perspective. Namely, we do not claim here that waste trade is the source of all the environmental and human health problems that waste produces. We claim that in those countries with a large burden due to bad practices and poor resources for waste management, importing any amount of waste will only aggravate their situation. This is illustrated by the fact that in Africa there are significant levels of soil pollution due to agricultural activities, mining, roadside emissions, automechanic workshops, their own refuse dumps and e-waste. 14 Then, when poor African countries like Nigeria, become a dumping ground for HW imported from abroad, 15 the situation become of a very high risk. In Africa there are 67,740 health-care facilities which generate 56,100-487,100 tonnes of medical waste per year. These global amounts are not exaggeratedly large, but the risk is very high considering that medical waste is rarely sorted which makes the amounts of HW much higher than in other parts of the world. 16,17 Then, when these countries receive large amounts of e-waste from abroad they do not have resources for dealing with its recycling. The consequences are elevated levels of e-waste pollutants in water, air, soil, dust, fish, vegetable, and human blood, urine, breast milk, producing headache, cough and chest pain, stomach discomfort, miscarriage, abnormal thyroid and reproductive function, reduction of gonadal hormone, and cancer in those involved with the processing of e-waste. 18 In Table SI. 7 we report the chemical fingerprints left by different types of waste according to an intensive bibliographic search carried out in this work. In Tables SI. 8, SI. 9 and SI. 10 we then report every individual waste category reported by the Basel Convention, which are on the types I-III considered in this work. We report the chemical fingerprints left by these waste based on the specific report on their contents at the Basel Convention web page.

Centrality of countries in the W4 networks
Here we introduce other networks metrics for waste types I, II, and III. Main countries which are closer to all countries/territories in the waste network for out-closeness centrality of type III (c). We highlight the first twelve hubs of each networks. Country codes belong to the ISO-alpha-2 standard. Map tiles by Bjorn Sandvik, under CC BY-SA 3.0 available at http://thematicmapping.org/downloads/world_borders.php. Figure SI. 7: Schematic illustration of the "congestion at arrival" (a) and "congestion at departure" (c) models and the time-evolution of the congestion propagation through the nodes using these models (b and d). Notice that in the congestion at arrival (panel b), node C reaches 50 % of congestion at a earlier time than A and B. In the congestion at departure (panel d), node A reaches 50 % of congestion earlier than B and C. Also notice that the ordering of congestion times at departure and arrival are not simply one the reverse of the other.

Theoretical modeling approach
The logistic dynamic model on a network is written as (see 39 for analysis in the case of Susceptible-Infected model, which is a particular case of the general model written here): where A ij are the entries of the adjacency matrix of the W4 for the pair of countries i and j. In matrix-vector form it becomes: with initial condition w (0) = w 0 ,where I N is the identity matrix of order N . This model can be rewritten as which is equivalent to We now consider a dynamics with non-locality by time or dynamic memory as described in the main text. To write the logistic model in this new context we start as follows. Let 0 < α < 1, then Then, we have which for the case of a network is written as We can rewrite (0.6) in a matrix-vector form: with the logarithm taken entrywise, and with initial condition w (0) = w 0 . In order to solve analytically the previous equation we apply the Lee-Tenneti-Eun (LTE) transformation 40 which produces the following linearized equation is an approximate solution to the fractional SI model,ŷ is the solution of (0.8) with initial conditionŷ (0) = g (x (0)), 1 is the all-ones vector, and b (w) := w + (1 − w) log (1 − w) . For convenience, we write Ω := diag (1 − w 0 ) , andÂ = AΩ. Then, we have proved that this approximate solutionŵ (t) is a non-divergent upper bound to the exact solution x(t).
We also proved that when all values of the initial condition are smaller than one, i.e., w 0 ⪯ 1, which means that at the starting point of the simulation no country is completely congested of waste, the solution of the fractional logistic waste congestion model iŝ This is important because if we consider the plausible case that the probability of getting congested at t = 0 is the same for every country, which mathematically is written as: w 0 = c N where c ∈ R + , we have that where γ = 1 − w 0 and we have used the fact that diag (1 − w (0)) = γI, where I is the identity matrix. The Mittag-Leffler function E α,1 ζA with ζ = (βt) 1/2 γ, which appears in the approximate solution of the congestion models described in the main text, belongs to the class of matrix functions of the adjacency matrix. 41 It can be written as 42-45 If we expand the first terms of this matrix function for a pair of countries v and w we get: The first term is different from zero only if the country v exports some amount of waste to country w. The second term accounts for the export of v to any country i, which then exports to w: v → i → w. The third term accounts for a chain of the type: v → i → j → w or of an interchange: v → w → v → w. In every case the amounts exported from one country to another are taken into account. Notice that such chains could be of infinite length, but their importance is diminished by the denominator of each particular term, given by the Euler gamma functions.
A centrality index, like the strengths (in-and out-) only take into account the contribution of exports/import between pairs of connected nodes in the network. In case that the country v exports some amount of waste to country w, the out-strength of v is given by the first term of the previous series expansion. However, this strength measures do not take into account the chains of lengths longer than one, such as v → i → w, or v → i → j → w. More importantly, if two countries v and w are not connected in the network, the strengths measures fail to account for possible indirect exports/imports between these two countries through an intermediary, such as in v → i → w.
This lack of correlation between the first order measures, like strength, and higher order ones are revealed by the plots (see   BF Heavy metals contamination of soils from informal settlements, peri-urban agriculture and unregulated waste dumping; problems with waste management producing heavy metals contamination and with impact on human health.

59-62
CN Heavy metals, VOC and POP pollution due to e-waste disposal and mismanagement with serious thread for human health; high contamination levels of PCB from equipments; emission and speciation of VOC from anthropogenic sources, ncluding high levels of BTEX; high levels of pollution from medical wastes and their incineration.

63-75
CD Heavy metals and POP contamination in river, estuary, and marine sediments from Atlantic Coast; impact of heavy metals on human health in children and adult populations; contamination of water resources and food chain by POP.

DJ
Reports of a shipment of containers with up to 20 metric tons of toxic chemicals were found leaking in the port of Djibouti with potential pollution by Arsenic. 80 ET Problems with uncontrolled waste disposal and heavy metals contamination of soils and waters in Addis Ababa; contamination by VOC in urban environment; high levels of pollution by POP, specially PCB and dioxins at different lcatins and levels of the trophic chain; seriuos problems of mismanagement of medical wastes with reported cases of hepatitis B and C directly related to them.

PK
Heavy metals pollution from diverse waste sources, including e-waste, recognized as an emerging problem and medical waste incineration; high levels of VOC, including BTEX in urban atmosphere; public health problems from hospital solid waste mismanagement.

138-145
PG Heavy metal water pollution in Depapre waters.

SN
Dramatic problems with household waste collection; reported waste contamination at different reservoirs by HM, mainly in the coast; environmental issues with biomedical waste disposal; 18 children died from a rapidly progressive central nervous system disease of unexplained origin in a community involved in the recycling of used lead-acid batteries; high levels of contamination with Pb in homes and soil in surrounding areas dedicated to car battery informal recycling, several children showed severe neurologic features of toxicity; high levels of VOC contamination at different environmental places.

SL
Heavy metals and POP contamination due to e-waste recycling; high levels of exposition to dioxins and furans; mismanagement of solid waste depositions with environmental and human health risk.

UZ
Pollution by heavy metals with impact on human health; contamination of soils with POP, particularly by PAHs.

159-161
Countries/territories without EPI Metal wastes and waste consisting of alloys of any of the following: Antimony, Arsenic, Beryllium, Cadmium, Lead, Mercury, Selenium, Tellurium, Thallium. A1020 Waste having as constituents or contaminants, excluding metal waste in massive form, any of the following: Antimony; antimony compounds, Beryllium; beryllium compounds, Cadmium; cadmium compounds, Lead; lead compounds, Selenium; selenium compounds, Tellurium; tellurium compounds A1030 Wastes having as constituents or contaminants any of the following: Arsenic; arsenic compounds, Mercury; mercury compounds, Thallium; thallium compounds A1040 Wastes having as constituents any of the following: Metal carbonyls, hexavalent chromium compounds A1050 Galvanic sludges A1060 Waste liquors from the pickling of metals A1070 Leaching residues from zinc processing, dust and sludges, such as jarosite, hematite, etc. A1080 Waste zinc residues, containing lead and cadmium in concentrations sufficient to exhibit Annex III characteristics A1090 Ashes from the incineration of insulated copper wire A1100 Dusts and residues from gas cleaning systems of copper smelters A1110 Spent electrolytic solutions from copper electrorefining and electrowinning operations A1120 Waste sludges, excluding anode slimes, from electrolyte purification systems in copper electrorefining and electrowinning operations A1130 Spent etching solutions containing dissolved copper A1140 Waste cupric chloride and copper cyanide catalysts A1150 Precious metal ash from incineration of printed circuit boards A1160 Waste lead-acid batteries, whole or crushed A1170 Unsorted waste batteries. Waste batteries containing Annex I constituents to an extent to render them hazardous A1180 Waste electrical and electronic assemblies or scrap containing components such as accumulators and other batteries included on list A, mercury-switches, glass from cathode-ray tubes and other activated glass and PCB capacitors, or contaminated with Annex I constituents (e.g., cadmium, mercury, lead, polychlorinated biphenyl) to an extent that they possess any of the characteristics contained in Annex III A1190 Waste metal cables coated or insulated with plastics containing or contaminated with coal tar, PCB, lead, cadmium, other organohalogen compounds or other Annex I constituents to an extent that they exhibit Annex III characteristics. category description A3010 Waste from the production or processing of petroleum coke and bitumen A3020 Waste mineral oils unfit for their originally intended use A3030 Wastes that contain, consist of or are contaminated with leaded anti-knock compound sludges A3040 Waste thermal (heat transfer) fluids A3050 Wastes from production, formulation and use of resins, latex, plasticizers, glues/adhesives A3060 Waste nitrocellulose A3070 Waste phenols, phenol compounds including chlorophenol in the form of liquids or sludges A3080 Waste ethers A3090 Waste leather dust, ash, sludges and flours when containing hexavalent chromium compounds or biocides A3100 Waste paring and other waste of leather or of composition leather not suitable for the manufacture of leather articles containing hexavalent chromium compounds or biocides A3110 Fellmongery wastes containing hexavalent chromium compounds or biocides or infectious substances A3120 Fluff-light fraction from shredding A3130 Waste organic phosphorous compounds A3140 Waste non-halogenated organic solvents A3150 Waste halogenated organic solvents A3160 Waste halogenated or unhalogenated non-aqueous distillation residues arising from organic solvent recovery operations A3170 Wastes arising from the production of aliphatic halogenated hydrocarbons (such as chloromethane, dichloro-ethane, vinyl chloride, vinylidene chloride, allyl chloride and epichlorhydrin) A3180 Wastes, substances and articles containing, consisting of or contaminated with polychlorinated biphenyl (PCB), polychlorinated terphenyl (PCT), polychlorinated naphthalene (PCN) or Polybrominated biphenyl (PBB), or any other polybrominated analogues of these compounds, at a concentration level of 50 mg/kg or more A3190 Waste tarry residues (excluding asphalt cements) arising from refining, distillation and any pyrolitic treatment of organic materials A3200 Bituminous material (asphalt waste) from road construction and maintenance, containing tar category description A4010 Wastes from the production, preparation and use of pharmaceutical products A4020 Clinical and related wastes; that is wastes arising from medical, nursing, dental, veterinary, or similar practices, and wastes generated in hospitals or other facilities during the investigation or treatment of patients, or research projects A4030 Wastes from the production, formulation and use of biocides and phytopharmaceuticals, including waste pesticides and herbicides which are off-specification, outdated, or unfit for their originally intended use A4040 Wastes from the manufacture, formulation and use of wood preserving chemicals A4050 Wastes that contain, consist of or are contaminated with any of the following: Inorganic cyanides, excepting precious-metal-bearing, residues in solid form containing traces of inorganic cyanides, organic cyanides A4060 Waste oils/water, hydrocarbons/water mixtures, emulsions A4070 Wastes from the production, formulation and use of inks, dyes, pigments, paints, lacquers, varnish A4080 Wastes of an explosive nature A4090 Waste acidic or basic solutions A4100 Wastes from industrial pollution control devices for cleaning of industrial off-gases A4110 Wastes that contain, consist of or are contaminated with any of the following: Any congenor of polychlorinated dibenzo-furan; Any congenor of polychlorinated dibenzo-p-dioxin A4120 Wastes that contain, consist of or are contaminated with peroxides A4130 Waste packages and containers containing Annex I substances in concentrations sufficient to exhibit Annex III hazard characteristics A4140 Waste consisting of or containing off specification or outdated chemicals corresponding to Annex I categories and exhibiting Annex III hazard characteristics A4150 Waste chemical substances arising from research and development or teaching activities which are not identified and/or are new and whose effects on human health and/or the environment are not known A4160 Spent activated carbon

PEIWS analysis of wastes types IV-VII
Following the same procedure described in Methods we build the PEIWS of the four types of waste IV-VII, which are illustrated in Fig. SI. 9. Using the same approach as for the waste types I-III we identify these countries at HRIHDW. In total in the four types of waste there are 29 countries at HRIHDW, 22 of which coincide with countries previously identified at HRIHDW for waste types I-III. The new countries at HRIHDW, i.e., not identified for types I-III, are Kazakhstan, Mongolia, Côte d'Ivoire, Saudi Arabia, Tanzania, Kenya and Oman. Wastes of types IV and VI are the ones with the largest number of countries at HRIHDW with 15 and 12, respectively, while types V and VII have 8 and 9 countries at HRIHDW, respectively. By continents, Africa is again the one having more countries at HRIHDW with 12, followed by Asia (9) and then Middle East and Europe with 4 each.