Computational and mathematical methods to estimate the basic reproduction number and final size for single-stage and multistage progression disease models for Zika with preventative measures
type: Item
instance of: scholarly article
title: Computational and mathematical methods to estimate the basic reproduction number and final size for single-stage and multistage progression disease models for Zika with preventative measures
zbMATH Open document ID: 1397.92669
DOI: 10.1155/2017/4290825
author: Y. Aharonov
published in: Computational \& Mathematical Methods in Medicine
publication date: 2018-08-27T00:00:00Z
review text: Summary: We present new mathematical models that include the impact of using selected preventative measures such as insecticide treated nets (ITN) in controlling or ameliorating the spread of the Zika virus. For these models, we derive the basic reproduction number and sharp estimates for the final size relation. We first present a single-stage model which is later extended to a new multistage model for Zika that incorporates more realistic incubation stages for both the humans and vectors. For each of these models, we derive a basic reproduction number and a final size relation estimate. We observe that the basic reproduction number for the multistage model converges to expected values for a standard Zika epidemic model with fixed incubation periods in both hosts and vectors. Finally, we also perform several computational experiments to validate the theoretical results obtained in this work and study the influence of various parameters on the models.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92-08
Mathematics Subject Classification ID: 92C60
zbMATH DE Number: 6925422
zbMATH Keywords: computational and mathematical methods
zbMATH Keywords: reproduction number
zbMATH Keywords: single-stage progression disease model
zbMATH Keywords: multistage progression disease model
zbMATH Keywords: Zika
zbMATH Keywords: preventative measures
Wikidata QID: Q40037590
describes a project that uses: ode23
describes a project that uses: ode45
describes a project that uses: Ode15s
describes a project that uses: ode113
describes a project that uses: Matlab
describes a project that uses: MATLAB ODE suite
describes a project that uses: ode23s
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/4290825
OpenAlex ID: W2749941382
cites work: Q4873545
cites work: The Kermack--McKendrick epidemic model revisited
cites work: The differential infectivity and staged progression models for the transmission of HIV
cites work: Q4692918
cites work: Estimation of the reproduction number of dengue fever from spatial epidemic data
cites work: Mathematical model of three age-structured transmission dynamics of chikungunya virus
cites work: Mathematical modelling of immune parameters in the evolution of severe dengue
cites work: Q2716352
cites work: Q4732342
cites work: Q4836464
cites work: On the definition and the computation of the basic reproduction ratio \(R_ 0\) in models for infectious diseases in heterogeneous populations
cites work: The MATLAB ODE Suite
description: scientific article; zbMATH DE number 6925422