A Model for Chagas Disease with Oral and Congenital Transmission

Coffield, Daniel J.; Spagnuolo, Anna Maria; Shillor, Meir; Mema, Ensela; Pell, Bruce; Pruzinsky, Amanda; Zetye, Alexandra

doi:10.1371/journal.pone.0067267

Cited by 39 publications

(40 citation statements)

References 32 publications

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“…where the weighted blood supply b supp is given in the table and the biting rate function, taken from [8], is…”

Section: A the Data Functions And Coefficientsmentioning

confidence: 99%

A Model for the Transmission of Chagas Disease with Random Inputs

Coffield

Kuttler²,

Qu³

et al. 2014

BIOMATH

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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.

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“…where the weighted blood supply b supp is given in the table and the biting rate function, taken from [8], is…”

Section: A the Data Functions And Coefficientsmentioning

confidence: 99%

A Model for the Transmission of Chagas Disease with Random Inputs

Coffield

Kuttler²,

Qu³

et al. 2014

BIOMATH

Self Cite

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“…However the model here differs in that the logistic term vanishes when the population is above the carrying capacity. For a survey of single species dynamics governed by delay differential equations, see [28] More recently, a mathematical model and simulations for the spread of Chagas disease in rural villages were presented in [9]. The model is an enhanced version of that in [33], because it includes additional terms involving effects of congenital transmission in humans and domestic mammals and oral transmission in domestic mammals.…”

Section: Coffield Et Al Steady State Stability Analysis Of a Chagmentioning

confidence: 99%

“…The model is an enhanced version of that in [33], because it includes additional terms involving effects of congenital transmission in humans and domestic mammals and oral transmission in domestic mammals. Here, we present a steady state stability analysis for a special version of the model in [9]: the case where the model has constant coefficients, rather than the more general case of seasonal coefficients.…”

Section: Coffield Et Al Steady State Stability Analysis Of a Chagmentioning

confidence: 99%

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Steady State Stability Analysis of a Chagas Disease Model

Coffield

Spagnuolo

2014

BIOMATH

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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 total population of 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 along with conditions for local asymptotic stability and partial results for global asymptotic stability. Numerical simulation results are presented, verifying the theoretical results.

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“…To this end, many mathematical models have been constructed (see e.g., Cohen and Gürtler, 2001;Castañera et al, 2003;Coffield et al, 2013;Nouvellet et al, 2015). However, all of these models utilize solely either the deterministic or the stochastic approach.…”

Section: Introductionmentioning

confidence: 99%

Modeling and simulation of multi-scale environmental systems with Generalized Hybrid Petri Nets

Herajy

Heiner

2015

Front. Environ. Sci.

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Predicting and studying the dynamics and properties of environmental systems necessitates the construction and simulation of mathematical models entailing different levels of complexities. Such type of computational experiments often require the combination of discrete and continuous variables as well as processes operating at different time scales. Furthermore, the iterative steps of constructing and analyzing environmental models might involve researchers with different background. Hybrid Petri nets may contribute in overcoming such challenges as they facilitate the implementation of systems integrating discrete and continuous dynamics. Additionally, the visual depiction of model components will inevitably help to bridge the gap between scientists with distinct expertise working on the same problem. Thus, modeling environmental systems with hybrid Petri nets enables the construction of complex processes while keeping the models comprehensible for researchers working on the same project with significantly divergent educational background. In this paper we propose the utilization of a special class of hybrid Petri nets, Generalized Hybrid Petri Nets (GHPN ), to model and simulate environmental systems exposing processes interacting at different time-scales. GHPN integrate stochastic and deterministic semantics as well as some other types of special basic events. To this end, we present a case study illustrating the use of GHPN in constructing and simulating multi-timescale environmental scenarios.Keywords: modeling and simulation, Hybrid Petri Nets, multi-scale environmental systems, Chagas disease, Triatoma infestans IntroductionThe process of constructing and analyzing environmental systems is increasingly becoming a complex procedure (Seppelt et al., 2009;Uusitalo et al., 2015). On the one hand, it can require the amalgamation of different simulation techniques to accurately and efficiently find a solution to the problem under consideration (see e.g., Gillet, 2008;Gregorio et al., 1999). On the other hand, complex environmental systems require the collection and analysis of various data and information that cannot be tackled by researchers coming from just one area of expertise (Seppelt et al., 2009).While the ordinary differential equations (ODEs) approach is widely used to construct and simulate many problems in the environmental domain, certain classes of such problems cannot be adequately addressed using this approach alone. For instance in Khoury et al. (2013) construct a simple, but elegant ODEs model to study food and population dynamics in honey bee colonies. However, such a continuous approach cannot capture the effect of seasonal variations Herajy and Heiner GHPN for multi-scale environmental systems on many parameters. Contrary, in Schmickl and Crailsheim (2007) and Russell et al. (2013) a discrete simulation of recurrence and difference equations has been deployed to emulate the discrete changes in bee population taking into account seasonal variations. Nevertheless, certain scenarios necessitate ...

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A Model for Chagas Disease with Oral and Congenital Transmission

Cited by 39 publications

References 32 publications

A Model for the Transmission of Chagas Disease with Random Inputs

A Model for the Transmission of Chagas Disease with Random Inputs

Steady State Stability Analysis of a Chagas Disease Model

Modeling and simulation of multi-scale environmental systems with Generalized Hybrid Petri Nets

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