Steady State Stability Analysis of a Chagas Disease Model

Coffield, Daniel J.; Spagnuolo, Anna Maria

doi:10.11145/j.biomath.2014.05.261

Cited by 4 publications

(1 citation statement)

References 31 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, there are parts of Latin America where the disease seems to be uncontrollable, such as the Bolivian Since insecticide spraying is essential in controlling the disease, there is considerable interest in optimizing the spraying schedules so as to make them as effective as possible in decreasing the domestic insect population. A basic model for the disease transmission dynamics that includes the effects of insecticide spraying was constructed and investigated in [31], and related issues were studied in [7], [9], [32]. Several applied Chagas disease transmission models have been developed, such as a deterministic model [11], a stochastic Markovian model [35], as well as a specific mathematical model to optimize spatio-temporal strategies to control the Chagas disease vectors [18].…”

Section: Introductionmentioning

confidence: 99%

A Model for the Transmission of Chagas Disease with Random Inputs

Coffield

Kuttler²,

Qu³

et al. 2014

BIOMATH

Self Cite

View full text Add to dashboard Cite

Abstract-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.

show abstract

Section: Introductionmentioning

confidence: 99%

A Model for the Transmission of Chagas Disease with Random Inputs

Coffield

Kuttler²,

Qu³

et al. 2014

BIOMATH

Self Cite

View full text Add to dashboard Cite

show abstract

Modeling the impact of non-human host predation on the transmission of Chagas disease

Dai,

Wu,

Jiang

et al. 2024

Mathematical Biosciences

View full text Add to dashboard Cite

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

et al. 2017

View full text Add to dashboard Cite

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) [27] 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].

show abstract

Steady State Stability Analysis of a Chagas Disease Model

Cited by 4 publications

References 31 publications

A Model for the Transmission of Chagas Disease with Random Inputs

A Model for the Transmission of Chagas Disease with Random Inputs

Modeling the impact of non-human host predation on the transmission of Chagas disease

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

Contact Info

Product

Resources

About