Dynamic of a TB-HIV Coinfection Epidemic Model with Latent Age
A coepidemic arises when the spread of one infectious disease stimulates the spread of another infectious disease. Recently, this has happened with human immunodeficiency virus (HIV) and tuberculosis (TB). The density of individuals infected with latent tuberculosis is structured by age since latenc...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/429567 |
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| _version_ | 1832555392403505152 |
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| author | Xiaoyan Wang Junyuan Yang Fengqin Zhang |
| author_facet | Xiaoyan Wang Junyuan Yang Fengqin Zhang |
| author_sort | Xiaoyan Wang |
| collection | DOAJ |
| description | A coepidemic arises when the spread of one infectious disease stimulates the spread of
another infectious disease. Recently, this has happened with human immunodeficiency virus (HIV)
and tuberculosis (TB). The density of individuals infected with latent tuberculosis is structured by age
since latency. The host population is divided into five subclasses of susceptibles, latent TB, active TB
(without HIV), HIV infectives (without TB), and coinfection class (infected by both TB and HIV). The
model exhibits three boundary equilibria, namely, disease free equilibrium, TB dominated equilibrium, and
HIV dominated equilibrium. We discuss the local or global stabilities of boundary equilibria. We
prove the persistence of our model. Our simple model of two synergistic infectious disease epidemics
illustrates the importance of including the effects of each disease on the transmission and progression
of the other disease. We simulate the dynamic behaviors of our model and give medicine explanations. |
| format | Article |
| id | doaj-art-c6036486b8b54b3d96809f0429b4dca3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c6036486b8b54b3d96809f0429b4dca32025-02-03T05:48:21ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/429567429567Dynamic of a TB-HIV Coinfection Epidemic Model with Latent AgeXiaoyan Wang0Junyuan Yang1Fengqin Zhang2Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, ChinaDepartment of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, ChinaDepartment of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, ChinaA coepidemic arises when the spread of one infectious disease stimulates the spread of another infectious disease. Recently, this has happened with human immunodeficiency virus (HIV) and tuberculosis (TB). The density of individuals infected with latent tuberculosis is structured by age since latency. The host population is divided into five subclasses of susceptibles, latent TB, active TB (without HIV), HIV infectives (without TB), and coinfection class (infected by both TB and HIV). The model exhibits three boundary equilibria, namely, disease free equilibrium, TB dominated equilibrium, and HIV dominated equilibrium. We discuss the local or global stabilities of boundary equilibria. We prove the persistence of our model. Our simple model of two synergistic infectious disease epidemics illustrates the importance of including the effects of each disease on the transmission and progression of the other disease. We simulate the dynamic behaviors of our model and give medicine explanations.http://dx.doi.org/10.1155/2013/429567 |
| spellingShingle | Xiaoyan Wang Junyuan Yang Fengqin Zhang Dynamic of a TB-HIV Coinfection Epidemic Model with Latent Age Journal of Applied Mathematics |
| title | Dynamic of a TB-HIV Coinfection Epidemic Model with Latent Age |
| title_full | Dynamic of a TB-HIV Coinfection Epidemic Model with Latent Age |
| title_fullStr | Dynamic of a TB-HIV Coinfection Epidemic Model with Latent Age |
| title_full_unstemmed | Dynamic of a TB-HIV Coinfection Epidemic Model with Latent Age |
| title_short | Dynamic of a TB-HIV Coinfection Epidemic Model with Latent Age |
| title_sort | dynamic of a tb hiv coinfection epidemic model with latent age |
| url | http://dx.doi.org/10.1155/2013/429567 |
| work_keys_str_mv | AT xiaoyanwang dynamicofatbhivcoinfectionepidemicmodelwithlatentage AT junyuanyang dynamicofatbhivcoinfectionepidemicmodelwithlatentage AT fengqinzhang dynamicofatbhivcoinfectionepidemicmodelwithlatentage |