Solving SEI model using non-standard finite difference and high order extrapolation with variable step length

A high-level method was obtained to solve the SEI model problem involving Symmetrization measures in numerical calculations through the Implicit Midpoint Rule method (IMR). It is obtained using Non-Standard Finite Difference Schemes (NSFD) with Extrapolation techniques combined. In solving differential equation problems numerically, the Extrapolated SEI model method is able to generate more accurate results than the existing numerical method of SEI model. This study aims to investigate the accuracy and efficiency of computing between Extrapolated One-Step Active Symmetry Implicit Midpoint Rule method (1ASIMR), Extrapolated One-Step Active Symmetry Implicit Midpoint Rule method (2ASIMR), Extrapolated One-Step Passive Symmetry Midpoint Rule method (1PSIMR) and the extrapolated Two-Step Passive Symmetry Midpoint Rule method (2PSIMR). The results show that the 1ASIMR method is the most accurate method. For the determination of the efficiency of 2ASIMR and 2PSIMR methods have high efficiency. At the end of the study, the results from the numerical method obtained show that Extrapolation using Non-Standard Finite Difference has higher accuracy than the existing Implicit Midpoint Rule method

NONSTANDARD FINITE DIFFERENCE SCHEMES FOR SOLVING A MODIFIED EPIDEMIOLOGICAL MODEL FOR COMPUTER VIRUSES

In this paper we construct two families of nonstandard finite difference (NSFD) schemes preserving the essential properties of a computer virus propagation model, such as positivity, boundedness and stability. The first family of NSFD schemes is constructed based on the nonlocal discretization and has first order of accuracy, while the second one is based on the combination of a classical Runge-Kutta method and selection of a nonstandard denominator function and it is of fourth order of accuracy. The theoretical study of these families of NSFD schemes is performed with support of numerical simulations. The numerical simulations confirm the accuracy and the efficiency of the fourth order NSFD schemes. They hint that the disease-free equilibrium point is not only locally stable but also globally stable, and then this fact is proved theoretically. The experimental results also show that the global stability of the continuous model is preserved

2nd International Conference on Numerical and Symbolic Computation

The Organizing Committee of SYMCOMP2015 – 2nd International Conference on Numerical and Symbolic Computation: Developments and Applications welcomes all the participants and acknowledge the contribution of the authors to the success of this event. This Second International Conference on Numerical and Symbolic Computation, is promoted by APMTAC - Associação Portuguesa de Mecânica Teórica, Aplicada e Computacional and it was organized in the context of IDMEC/IST - Instituto de Engenharia Mecânica. With this ECCOMAS Thematic Conference it is intended to bring together academic and scientific communities that are involved with Numerical and Symbolic Computation in the most various scientific area

Models of Delay Differential Equations

This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineerin

How Environmental Change Will Impact Mosquito-Borne Diseases

Mosquitos, the most lethal species throughout human history, are the most prevalent source of vector-borne diseases and therefore a major global health burden. Mosquito-borne disease incidence is expected to shift with environmental change. These changes can be predicted using species distribution models. With the wide variety of methods used for models, consensus for improving accuracy and comparability is needed. A comparative analysis of three recent modeling approaches revealed that integrating modeling techniques compensates for trade-offs associated with a singular approach. An area that represents a critical gap in our ability to predict mosquito behavior in response to changing climate factors, such as temperature, is evolutionary adaptive potential. Evolutionary studies for mosquitos have documented rapid evolutionary change in photoperiodic traits. Further research on evolutionary adaptive potential for mosquito thermal tolerances using longitudinal studies in conjunction with genomic approaches will allow for more realistic parameterization of mosquito biological processes. One of the primary factors driving disease patterns is urbanization. Urban areas are already highly impacted by climate-related health issues and offer a wide variety of potential aquatic habitats for breeding, thereby presenting vulnerable targets for mosquito populations. Mosquito-borne diseases have been historically underrepresented in urban health planning, and with projected increases in habitat suitability for temperate areas such as the U.S., promoting awareness of this issue constitutes a major health priority for the future. Integrating mosquito control policies into urban planning and design, such as concomitant strategies for elimination in green space development, will be highly beneficial in mitigating adverse health outcomes

Variable step length algorithms with high-order extrapolated non-standard finite difference schemes for a SEIR model.

[EN]n the present manuscript, higher-order methods are derived to solve a SEIR model for malware propagation. They are obtained using extrapolation techniques combined with nonstandard finite difference (NSFD) schemes used in Jansen and Twizell (2002). Thus, the new algorithms are more efficient computationally, and are dynamically consistent with the continuous model. Later, different procedures are considered to control the error in the discrete schemes. Numerical experiments are provided to illustrate the theory, and for the comparison of the different strategies in the adaptation of the variable step length

A data-driven epidemic model to analyse the course of covid-19 in the Veneto region

The current COVID-19 pandemic is an unprecedented global health crisis, with severe economic impacts and social damages. Mathematical models are playing an important role in this ongoing emergency, providing scientific support to inform public policies worldwide. In this thesis work, an epidemic model for the spread of the novel Coronavirus disease in the Veneto region has been proposed. Starting from the available local Health System data to examine past year contagion numbers and other features potentiality, a SEIQRD (Susceptible Exposed Infected Quarantined Removed Deceased) compartmental schema has been designed generalizing the classic SIR model. Then, the infection dynamics have been practically implemented in two versions: as a Deterministic Equation-based formulation and as an Agent-based model. While the former has been maintained simple and computationally inexpensive in order to serve as a baseline and to quickly provide parameter estimates, for the latter a detailed metapopulation of agents with personalized attributes and network of contacts has been developed to recreate as realistic as possible simulations. Once these models have been trained and validated, they could became valuable tools for various types of analysis and predictions. In particular, the agent-based version, thanks to its flexibility as well as to its higher resolution, could be exploited for exclusive a posteriori evaluations of the effectiveness of the adopted containment measures in reducing the pandemic in Veneto.ope