Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency
Vaccine-induced protection is substantial to control, prevent, and reduce the spread of infectious diseases and to get rid of infectious diseases. In this paper, we propose an SVEIR epidemic model with age-dependent vaccination, latency, and infection. The model also considers that the waning vaccin...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/8479638 |
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| author | Rodrigue Yves M’pika Massoukou Suares Clovis Oukouomi Noutchie Richard Guiem |
| author_facet | Rodrigue Yves M’pika Massoukou Suares Clovis Oukouomi Noutchie Richard Guiem |
| author_sort | Rodrigue Yves M’pika Massoukou |
| collection | DOAJ |
| description | Vaccine-induced protection is substantial to control, prevent, and reduce the spread of infectious diseases and to get rid of infectious diseases. In this paper, we propose an SVEIR epidemic model with age-dependent vaccination, latency, and infection. The model also considers that the waning vaccine-induced immunity depends on vaccination age and the vaccinated individuals fall back to the susceptible class after losing immunity. The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. The global dynamics of the model is established through construction of appropriate Lyapunov functionals and application of Lasalle’s invariance principle. As a result, the global stability of the infection-free equilibrium and endemic equilibrium is obtained and is fully determined by the basic reproduction number R0. |
| format | Article |
| id | doaj-art-f2216725995e43c8b8f840690cf18ea2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f2216725995e43c8b8f840690cf18ea22025-02-03T01:10:35ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/84796388479638Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and LatencyRodrigue Yves M’pika Massoukou0Suares Clovis Oukouomi Noutchie1Richard Guiem2School of Mathematical and Statistical Sciences, North-West University, Mafikeng campus, Private Bag X2046, Mmabatho 2735, South AfricaSchool of Mathematical and Statistical Sciences, North-West University, Mafikeng campus, Private Bag X2046, Mmabatho 2735, South AfricaSchool of Mathematical and Statistical Sciences, North-West University, Mafikeng campus, Private Bag X2046, Mmabatho 2735, South AfricaVaccine-induced protection is substantial to control, prevent, and reduce the spread of infectious diseases and to get rid of infectious diseases. In this paper, we propose an SVEIR epidemic model with age-dependent vaccination, latency, and infection. The model also considers that the waning vaccine-induced immunity depends on vaccination age and the vaccinated individuals fall back to the susceptible class after losing immunity. The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. The global dynamics of the model is established through construction of appropriate Lyapunov functionals and application of Lasalle’s invariance principle. As a result, the global stability of the infection-free equilibrium and endemic equilibrium is obtained and is fully determined by the basic reproduction number R0.http://dx.doi.org/10.1155/2018/8479638 |
| spellingShingle | Rodrigue Yves M’pika Massoukou Suares Clovis Oukouomi Noutchie Richard Guiem Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency Abstract and Applied Analysis |
| title | Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency |
| title_full | Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency |
| title_fullStr | Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency |
| title_full_unstemmed | Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency |
| title_short | Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency |
| title_sort | global dynamics of an sveir model with age dependent vaccination infection and latency |
| url | http://dx.doi.org/10.1155/2018/8479638 |
| work_keys_str_mv | AT rodrigueyvesmpikamassoukou globaldynamicsofansveirmodelwithagedependentvaccinationinfectionandlatency AT suaresclovisoukouominoutchie globaldynamicsofansveirmodelwithagedependentvaccinationinfectionandlatency AT richardguiem globaldynamicsofansveirmodelwithagedependentvaccinationinfectionandlatency |