Improvements in socio-economic conditions, parental education, water supply, and decrease in the global burden of disease in Assis Brasil were observed between the studied periods. However, population growth in the period from 2003 to 2010 was higher than usual. The municipality did not have adequate urban infrastructure to receive this demand, resulting in increased areas of illegal settlements. This may partly explain the increased presence of open sewage observed when comparing periods.
In this study, undernutrition rates did not change significantly over the decade. In 2003, undernutrition prevalence in Assis Brasil (7.0%) was similar to the Brazilian average of 8.7% , but while in 2006 the national average decreased to 6.7% , in the city of Assis Brasil, undernutrition rates remained high (12.2%) until 2010.
Obesity occurs more often in the first years of the life cycle, between 5 and 6 years of age, and in adolescence [20, 21]. In the present study, the prevalence of overweight increased from 1% to 6% between 2003 and 2010, reaching the national average identified in PNDS 2006 . This may reflect an increasing growth in children’s overweight and a future public health problem for the region. A possible explanation for this phenomenon is undernutrition early in life due to poor maternal nutrition and inadequate nutrition in early childhood, predisposing the body to store fat when eating foods rich in carbohydrates and fats. .
Another explanation for the overweight increase is the nutrition transition. The name “ nutrition transition” means a change in nutritional patterns related to food intake resulting from changes in social, economic and demographic status that affect health . According to Batista Filho and Rissin , the nutrition transition is a process characterised by four stages. In the first stage, the disappearance of acute and severe protein malnutrition related to protein intake deficiency is observed. In the second stage the disappearance of protein-energy malnutrition characterised as insufficient intake of calories and nutrients occurs. The third phase is characterised by the appearance of the binomial overweight/obesity on a population scale, caused by excessive food intake associated with increasing sedentariness. And the last stage of the transition is set in the correction of short stature, since there is no longer a poor intake of nutrients .
Several authors have reported that the process of demographic and economic transition observed in developing countries such as Brazil, contributes to the nutrition transition [23–25]. Reported studies show that Brazil is currently in the fourth stage of the nutritional transition process. However, this process is not uniform, and Assis Brasil, which is located in an underdeveloped region of the country, is still between the second and third stages, with increased overweight rates, but sustained chronic undernutrition. This is suggested by the high prevalence of low HAZ and high WHZ, as found in this study.
The process of nutritional transition is marked by the intake of a high calorie diet, rich in saturated fat and refined carbohydrates, which are characteristics of most industrialized foods, as well as by low intake of complex carbohydrates and fibers. The implementation of the Interoceanic Highway may have promoted the arrival of new foods from other regions of Brazil and Peru. When assessing the perception of the changes brought by BR-137 (Transoceanic Highway) to Assis Brasil residents in 2010, Martins et al. (unpublished observations) found that 89.7% of respondents reported improvements in the variety and availability of food and 8.8.5% reported improvements in the local market. Poor logistic access to Assis Brasil before the BR-317 was related to the unavailability of perishable foods at home. In addition, preliminary results from the Feeding Infants and Toddlers Study (FITS) confirm an excessive intake of industrialised food by children at this age .
Factors associated with undernutrition were mostly related to socio-economic status (wealth index, living conditions and schooling and number of pregnancies) and maternal height. Similar findings from 47 countries suggested that low height-for-age led to a greater association with socio-economic inequality than did low weight-for-height . A comparison of national nutritional surveys corroborate this information, describing that 21.7% of the reduction in the prevalence of child malnutrition between 1996 and 2006 can be attributed to the increasing purchasing power of Brazilian families. The government is partly responsible for this increase by granting benefits to mothers or guardians in poorer families .
The presence of open sewage was associated at a distal level with undernutrition in 2010. This has been reported elsewhere [28, 29]. Souza et al. (2012), while assessing malnutrition in two municipalities in the state of Acre in 2003, found that children exposed to open sewage near home were more likely to show low height-for-age in relation to the unexposed ones . When analysing national surveys, Monteiro et al.  also confirmed the association between inadequate sanitation and undernutrition. The possible biological relationship between undernutrition and open sewage is the increase in the number of cases of diarrhoea and intestinal parasitosis as well as other morbidities, resulting in growth retardation.
For the year 2003, poor maternal education levels showed greater association with low height-for-age than did socio-economic variables. Other studies on the relation between social and environmental conditions and malnutrition in São Paulo, Belo Horizonte, Maceió and Rio Grande do Sul also showed this association [31–34]. This relationship may result from the basic information on the importance of personal and household hygiene habits and practices of adequate nutrition for child growth and development. Drachler et al.  reported that the mother figure represents the bond between children and the environment, besides the fact that it is also the mother who usually decides on her family’s eating habits and on hygiene and immunization care. In 2010, an increase in maternal educational levels was observed, and it was not associated with undernutrition anymore.
In this study, for the year 2003, each new pregnancy increased the chance of an already existing child under 5 years of age to develop low height-for-age by 35%. Eastwood and Lipton  showed that, in families with low purchasing power, the impact of high fertility on the family income was more pronounced. Therefore, multiple pregnancies may have had an impact on socio-economic conditions in 2003, thus contributing to less food available and higher levels of undernutrition.
The effect of maternal height in child height can be explained as a biological relationship and, at the same time, as the result of socio-economic long-standing unfavorable conditions that had affected the mother in the past and are presently affecting their children as well. Previous studies have also shown this association between maternal height and stunting [31, 37, 38], and between maternal height and poverty and adverse socio-environmental conditions. Therefore, maternal short stature can predict undernutrition in children [31, 37, 38].
Although the prevalence of anemia and intestinal parasitosis was higher in undernourished children, these two morbidities were not associated with undernutrition in the final model possibly because they have similar associated factors and are not the cause of undernutrition per se. Some studies have already reported that inadequate sanitary conditions are associated with anaemia [39, 40] as well as undernutrition in children [28, 29].
Overweight in Assis Brasil was associated with child age, time of residence in the town and maternal BMI. The inverse association between age and overweight, found in this study, has also been reported by other Brazilian studies [41–43]. A study conducted in southern Brazil  reported a negative trend between age and overweight and obesity, which is possibly explained by the result of increased physical activity throughout the years, but no confirmatory studies have been published so far.
While low maternal height was associated with undernutrition, maternal overweight was a predictor of child overweight in this study as well. This is a common association reported extensively elsewhere [35, 44–49]. According to Maffeis et al. , the main risk factor for childhood obesity is still parental' obesity, occurring as a result of genetic representation concomitant with environmental influences. However, the mother is the main agent in determining the dietary habits adopted by a child, since she is the main individual involved in the selection and preparation of food .
In 2010, the length of time during which the mother had been living in the municipality was associated with overweight children. Each year of maternal residence in the municipality increased the chance of a child′s being overweight by 7%. The most likely hypothesis would be the rural exodus promoted by the Transoceanic Highway or the migration of people from other municipalities with poor conditions in search of better living conditions and the contact with industrialised food rich in fat and carbohydrates. This hypothesis is supported by three main findings: approximately 19.8% of the children were born outside the urban area and migrated to it when they were between 1 and 5 years old; undernutrition among children born in rural areas was high in this study, and overweight prevalence was higher in children whose families had been living in the urban area for a longer periods.
The main limitation of this study is that the cross-sectional design precludes a cause-and-effect relationship between the studied variables. Therefore, the associated factors observed should be interpreted as associations between events, and not as risk factors. Another limitation is that the population size is small for detecting events and therefore there may be an overestimation of the strengths of the associations described. This must be taken into account when interpreting results. Finally, not all variables studied in 2010 were investigated in 2003, so we may not have been able to detect all possible associated factors in 2003, such as the number of years of maternal residency in the urban area.