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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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2018/4168061 |
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| _version_ | 1832559746489516032 |
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| author | Stanislas Ouaro Ali Traoré |
| author_facet | Stanislas Ouaro Ali Traoré |
| author_sort | Stanislas Ouaro |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-22b89936cb714364aeddd692d82e5753 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-22b89936cb714364aeddd692d82e57532025-02-03T01:29:17ZengWileyInternational 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 |
| spellingShingle | Stanislas Ouaro Ali Traoré On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination International Journal of Differential Equations |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2018/4168061 |
| work_keys_str_mv | AT stanislasouaro ontheglobaldynamicsofavectorbornediseasemodelwithageofvaccination AT alitraore ontheglobaldynamicsofavectorbornediseasemodelwithageofvaccination |