Volume 36, Issue 2
Analysis of an Epidemic Model with Crowley-Martin Incidence Rate and Holling Type II Treatment

Liuqing Yang & Fengying Wei

Ann. Appl. Math., 36 (2020), pp. 204-220.

Published online: 2020-08

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We propose an epidemic model consisting five compartments within a total population with Crowley-Martin incidence rate and Holling type II treatment, where total population is separated by the susceptible, the vaccinated, the exposed, the infected and the removed in this paper. We firstly prove that the epidemic model admits a unique global positive solution by contradiction. We then find out that diseases tend to extinction provided that the basic reproduction number is less than one. Moreover, the sufficient conditions of persistence for infectious diseases are obtained by constructing suitable Lyapunov functions.

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@Article{AAM-36-204, author = {Yang , Liuqing and Wei , Fengying}, title = {Analysis of an Epidemic Model with Crowley-Martin Incidence Rate and Holling Type II Treatment}, journal = {Annals of Applied Mathematics}, year = {2020}, volume = {36}, number = {2}, pages = {204--220}, abstract = {

We propose an epidemic model consisting five compartments within a total population with Crowley-Martin incidence rate and Holling type II treatment, where total population is separated by the susceptible, the vaccinated, the exposed, the infected and the removed in this paper. We firstly prove that the epidemic model admits a unique global positive solution by contradiction. We then find out that diseases tend to extinction provided that the basic reproduction number is less than one. Moreover, the sufficient conditions of persistence for infectious diseases are obtained by constructing suitable Lyapunov functions.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/18098.html} }
TY - JOUR T1 - Analysis of an Epidemic Model with Crowley-Martin Incidence Rate and Holling Type II Treatment AU - Yang , Liuqing AU - Wei , Fengying JO - Annals of Applied Mathematics VL - 2 SP - 204 EP - 220 PY - 2020 DA - 2020/08 SN - 36 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/18098.html KW - epidemic model, Crowley-Martin incidence rate, extinction, persistence. AB -

We propose an epidemic model consisting five compartments within a total population with Crowley-Martin incidence rate and Holling type II treatment, where total population is separated by the susceptible, the vaccinated, the exposed, the infected and the removed in this paper. We firstly prove that the epidemic model admits a unique global positive solution by contradiction. We then find out that diseases tend to extinction provided that the basic reproduction number is less than one. Moreover, the sufficient conditions of persistence for infectious diseases are obtained by constructing suitable Lyapunov functions.

Liuqing Yang & Fengying Wei. (2020). Analysis of an Epidemic Model with Crowley-Martin Incidence Rate and Holling Type II Treatment. Annals of Applied Mathematics. 36 (2). 204-220. doi:
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