Abstract
Chagas disease is caused by the parasite Trypanosoma cruzi, which is spread primarily by domestic vectors in the reduviid family. This work presents a model of the dynamics of Chagas disease in a rural village. The model consists of a nonlinear delay logistic-type differential equation for the population of total vectors and three nonlinear differential equations for the populations of infected vectors, infected humans, and infected domestic mammals. Steady state solutions for the model are derived and analyzed. Stability numbers are provided with necessary and sufficient conditions for local asymptotic stability and partial results for global asymptotic stability. Numerical simulation results are presented, verifying the theoretical results.
Highlights
Chagas disease is caused by the parasite Trypanosoma cruzi
Two mathematical models [33], [34], each consisting of four nonlinear differential equations, have been recently used to study the dynamics of Chagas disease transmission
We model the total number of vectors in the village houses using a delay differential equation, and we model the infected vectors, infected humans, and infected domestic mammals using ordinary differential equations
Summary
Chagas disease is caused by the parasite Trypanosoma cruzi. It leads to organ deformity and early death in one third of the 8-10 million individuals infected throughout Latin America [24],. Additional control measures are treatment for acute Chagas disease and congenital transmission cases [17]. Two mathematical models [33], [34], each consisting of four nonlinear differential equations, have been recently used to study the dynamics of Chagas disease transmission. In [34], a delayed Nicholson’s blowfly-type term is used for the growth of vectors, whereas in [33], a delay logistic term represents the growth rate of the vectors The former allows control of the maximum growth rate, and the latter allows control over the vector carrying capacity in the village houses and a vector death rate due to overpopulation beyond the carrying capacity. A mathematical model and simulations for the spread of Chagas disease in rural villages were presented in [9].
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