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Simulations of a logistic-type model with delays for Chagas disease with insecticide spraying

International Journal of Biomathematics 2017年第3期10卷 41-60页

作者： Nofe Al-Asuoad Tyler Pleasant Meir Shillor hrishikesh munugala Daniel J. Coffield Jr. Anna Maria Spagnuolo Department of Mathematics and Statistics Oakland University Rochester MI 48309 USA Harrison High School MI USA Novi High School Novi MI 48375 USA Mathematics Department University of Michigan-Flint Flint MI 48502 USA

This work studies and numerically simulates a logistic-type model for the dynamics of Chagas disease, which is caused by the parasite T. cruzi and affects millions of humans and domestic mammals throughout rural areas in Central and South America. A basic model for the disease dynamics that includes insecticide spraying was developed in Spagnuolo et al. （2010） [271 and consists of a delay-differential equation for the vectors and three nonlinear ordinary differential equations for the populations of the infected vectors, infected humans and infected domestic mammals. In this work, the vector equation is modified by using a logistic term with zero, one or two delays or time lags. The aim of this study is three-fold： to numerically study the effects of using different numbers of delays on the model behavior; to find if twice yearly insecticide spraying schedules improve vector control; and to study the sensitivity of the system to the delays in the case of two delays, by introducing randomness in the delays. It is found that the vector equation with different number of delays has very different solutions. The ＂best＂ day of spraying is the middle of Spring and twice annual sprayings cause only minor improvements in disease control. Finally, the model is found to be insensitive to the values of the delays, when the delays are randomly distributed within rather narrow intervals or ranges centered on the parameter values used in Coffield et al. （2014） [8].

关键词： Chagas disease logistic equation with delays epidemic dynamics nonlinear dynamical system simulations.

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