Modeling diseases with latency and relapse
A general mathematical model for a disease with an exposed(latent) period and relapse is proposed. Such a model isappropriate for tuberculosis, including bovine tuberculosis incattle and wildlife, and for herpes. For this model with ageneral probability of remaining in the exposed class, the bas...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2007-01-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.205 |
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| Summary: | A general mathematical model for a disease with an exposed(latent) period and relapse is proposed. Such a model isappropriate for tuberculosis, including bovine tuberculosis incattle and wildlife, and for herpes. For this model with ageneral probability of remaining in the exposed class, the basicreproduction number $\R_0$ is identified and its thresholdproperty is discussed. In particular, the disease-free equilibriumis proved to be globally asymptotically stable if $\R_01$, and the disease is shown to be uniformly persistentwith the infective population size either approaching oroscillating about the endemic level. Numerical simulations (forparameters appropriate for bovine tuberculosis in cattle) with$\mathcal{R}_0>1$ indicate that solutions tend to this endemicstate. |
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| ISSN: | 1551-0018 |