Anna Maria Spagnuolo

A model for Chagas disease with controlled spraying

Chagas disease is a vector-borne parasitic disease that infects mammals, including humans, through much of Latin America. This work presents a mathematical model for the dynamics of domestic transmission in the form of four coupled nonlinear differential equations. The four equations model the number of domiciliary vectors, the number of infected domiciliary vectors, the number of infected humans, and the number of infected domestic animals. The main interest of this work lies in its study of the effects of insecticide spraying and of the recovery of vector populations with cessation of spraying. A novel aspect in the model is that yearly spraying, which is currently used to prevent transmission, is taken into account. The models predictions for a representative village are discussed. In particular, the model predicts that if pesticide use is discontinued, the vector population and the disease can return to their pre-spraying levels in approximately 5–8 years.

A Model for Chagas Disease with Oral and Congenital Transmission

This work presents a new mathematical model for the domestic transmission of Chagas disease, a parasitic disease affecting humans and other mammals throughout Central and South America. The model takes into account congenital transmission in both humans and domestic mammals as well as oral transmission in domestic mammals. The model has time-dependent coefficients to account for seasonality and consists of four nonlinear differential equations, one of which has a delay, for the populations of vectors, infected vectors, infected humans, and infected mammals in the domestic setting. Computer simulations show that congenital transmission has a modest effect on infection while oral transmission in domestic mammals substantially contributes to the spread of the disease. In particular, oral transmission provides an alternative to vector biting as an infection route for the domestic mammals, who are key to the infection cycle. This may lead to high infection rates in domestic mammals even when the vectors have a low preference for biting them, and ultimately results in high infection levels in humans.

A logistic delay differential equation model for Chagas disease with interrupted spraying schedules

This work studies a mathematical model for the dynamics of Chagas disease, a parasitic disease that affects humans and domestic mammals throughout rural areas in Central and South America. It presents a modified version of the model found in Spagnuolo et al. [A model for Chagas disease with controlled spraying, J. Biol. Dyn. 5 (2011), pp. 299–317] with a delayed logistic growth term, which captures an overshoot, beyond the vector carrying capacity, in the total vector population when the blood meal supply is large. It studies the steady states of the system in the case of constant coefficients without spraying, and the analysis shows that for given-averaged parameters, the endemic equilibrium is stable and attracting. The numerical simulations of the model dynamics with time-dependent coefficients are shown when interruptions in the annual insecticide spraying cycles are taken into account. Simulations show that when there are spraying schedule interruptions, spraying may become ineffective when the blood meal supply is large.

A Framework for Running the ADCIRC Discontinuous Galerkin Storm Surge Model on a GPU

Abstract Hybrid architectures utilizing GPUs provide a unique opportunity in a high performance computing environment. However, there are many legacy codes, particularly written in Fortran, that can not take immediate advantage of GPUs. Furthermore, many of these codes are under active development and so completely rewriting the code may not be an option. The advanced circulation and storm surge finite element model (ADCIRC) is one such code base. In this paper we present our semi-automatic methodology for porting portions of ADCIRC to run on the GPU and some preliminary scaling results of these subroutines. We have implemented a C++ array class and pre-processor macros to create a type of application framework to simplify the conversion and maintenance tasks. This allows the C++ syntax to be similar to Fortran, to provide for a more straight forward syntactical conversion from the original Fortran to C++ and simplified calling conventions between the two. After the necessary subroutines are converted to the C++ framework, the CUDA library can be easily used and also we are able to provide a simplified abstraction layer for accessing basic GPU functionality. For example, the problem of transferring the correct data on/o_ the GPU is addressed by our framework by a one time code change and a script to resolve data dependencies. Although it is currently specific to ADCIRC, our framework provides a starting point for utilizing GPUs with legacy Fortran codes, from which more specific GPU optimizations can be implemented.

Analysis of a multiple-porosity model for single-phase flow through naturally fractured porous media

A derivation of a multiple-porosity model for the flow of a single phase, slightly compressible fluid in a multiscale, naturally fractured reservoir is presented by means of recursive use of homagnetization theory. We obtain a model which generalizes the double-porosity model of Arbogast et al. (1990) to a flow system with an arbitrary finite number of scales.

Numerical simulations of vehicle platform stabilization

A new model for low-power active control of automotive suspension is described and numerically simulated. It is based on the vertically compressed horizontally sliding spring (VeCHSS) and is in the form of a nonlinear coupled system of ordinary differential equations. The numerical simulations indicate that when the system has one steady state, it is stable; when there are three steady states two are stable and the middle one is unstable. However, when there are two steady states, both are unstable, although the system trajectory is shown to be bounded. The simulations also indicate that the system, without any controls, can follow a periodic road profile well.

Modeling HIV-1 dynamics and the effects of decreasing activated infected T-cell count by filtration

Over the past 10 years mathematical models have been developed using differential equations for the progression of HIV-1 to AIDS in an infected patient. Additional terms and formulations are presented over time, as the disease is better understood. Experimentation has been used to obtain many of the modeling parameters. These previous works focus primarily on modeling the progression of the disease, some with intervention such as HAART drugs. Attempts have been made to filter HIV-1 and HIV-1-infected T-cells from the blood. A model is developed that characterizes the rate of filtrations impact on disease progression. Such studies could be also used to investigate the impact of an implantable HIV-1 filter. Proliferation rates of actively and latently infected T-cells are significant and have been incorporated into the models developed in this paper.

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

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...