A Model for the Transmission of Chagas Disease with Random Inputs

In this work we study and simulate a model for the dynamics of Chagas disease that includes randomness in some of the system coefficients. The disease, caused by the parasite T. cruzi, affects 8-10 million humans throughout rural areas in the Americas. A basic model for the disease dynamics, which consists of four nonlinear differential equations for the populations of the vectors, infected vectors, humans, and domestic animals was developed in Spagnuolo et al., (2009). Here, the model is modified by using a logistic term with two delays for vector population growth and extended to include random coefficients, reflecting the uncertainty in the determination of their values. The existence of the unique local solution for the model as a stochastic process is established. Numerical simulations are performed to conduct sensitivity analysis on seven of the model parameters. Variations in two of the model parameters lead to significant changes in the number of infected humans and infected domestic mammals, indicating that these parameters need to be accurately obtained.

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