On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination

On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination

We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease...

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Main Authors: Stanislas Ouaro, Ali Traoré
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2018/4168061
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spelling doaj-22b89936cb714364aeddd692d82e57532020-11-25T00:57:38ZengHindawi LimitedInternational Journal of Differential Equations1687-96431687-96512018-01-01201810.1155/2018/41680614168061On the Global Dynamics of a Vector-Borne Disease Model with Age of VaccinationStanislas Ouaro0Ali Traoré1LAboratoire de Mathématiques et Informatique (LAMI), Unité de Formation et de Recherche en Sciences Exactes et Appliquées, Département de Mathématiques, Université Ouaga I Pr Joseph KI-ZERBO, BP 7021, Ouagadougou, Burkina FasoLAboratoire de Mathématiques et Informatique (LAMI), Unité de Formation et de Recherche en Sciences Exactes et Appliquées, Département de Mathématiques, Université Ouaga I Pr Joseph KI-ZERBO, BP 7021, Ouagadougou, Burkina FasoWe study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable; that is, the disease dies out, while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable, which means that the disease persists in the population. Using the basic reproduction number, we derive a vaccination coverage rate that is required for disease control and elimination.http://dx.doi.org/10.1155/2018/4168061
collection DOAJ
language English
format Article
sources DOAJ
author Stanislas Ouaro
Ali Traoré
spellingShingle Stanislas Ouaro
Ali Traoré
On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination
International Journal of Differential Equations
author_facet Stanislas Ouaro
Ali Traoré
author_sort Stanislas Ouaro
title On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination
title_short On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination
title_full On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination
title_fullStr On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination
title_full_unstemmed On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination
title_sort on the global dynamics of a vector-borne disease model with age of vaccination
publisher Hindawi Limited
series International Journal of Differential Equations
issn 1687-9643
1687-9651
publishDate 2018-01-01
description We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable; that is, the disease dies out, while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable, which means that the disease persists in the population. Using the basic reproduction number, we derive a vaccination coverage rate that is required for disease control and elimination.
url http://dx.doi.org/10.1155/2018/4168061
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AT alitraore ontheglobaldynamicsofavectorbornediseasemodelwithageofvaccination
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