Calculating epidemiological measures of infection by Trypanosoma cruzi, the causative agent of Chagas disease, is complex, because it involves several species, different stages of infection in humans and multiple transmission routes. Using the next-generation matrix method, we analysed a model which considers the three stages of human infection, triatomines and dogs (the main domestic reservoirs of T. cruzi when triatomines are present) and the main transmission routes. We derived R 0 and type-reproduction numbers T. We deduced formulas for the number of new infections generated through each transmission route by each infected individual. We applied our findings in Argentine Gran Chaco. The expressions achieved allowed quantifying the high infectivity of dogs and emphasizing the epidemiological importance of the long and asymptomatic chronic indeterminate stage in humans in the spread of the infection. According to the model, it is expected that one infected human infects 21 triatomines, that 100 infected triatomines are necessary to infect one human and 34 to infect a dog, and that each dog infects on average one triatomine per day. Our results may allow quantifying the effect of control measures on infected humans, triatomines and dogs (or other highly infected vertebrate) or on a specific route of transmission, in other scenarios.
Transmission of Trypanosoma cruzi, the causal agent of Chagas disease, has expanded from rural endemic to urban areas due to migration. This so-called urban Chagas is an emerging health problem in American, European, Australian and Japanese cities. We present a mathematical model to analyse the dynamics of urban Chagas to better understand its epidemiology. The model considers the three clinical stages of the disease and the main routes of inter-human transmission. To overcome the complexities of the infection dynamics, the next-generation matrix method was developed. We deduced expressions which allowed estimating the number of new infections generated by an infected individual through each transmission route at each disease stage, the basic reproduction number and the number of individuals at each disease stage at the outbreak of the infection. The analysis was applied to Buenos Aires city (Argentina). We estimated that 94% of the new infections are generated by individuals in the chronic indeterminate stage. When migration was not considered, the infection disappeared slowly and R0 = 0.079, whereas when migration was considered, the number of individuals in each stage of the infection tended to stabilize. The expressions can be used to estimate different numbers of infected individuals in any place where only inter-human transmission is possible.
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