|
| ANALYSIS OF AN EPIDEMIC MODEL WITH CROWLEY-MARTIN INCIDENCE RATE AND HOLLING TYPE II TREATMENT |
| Liuqing Yang,Fengying Wei |
| (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, Fujian, PR China) |
| DOI： |
| Abstract: |
| We propose an epidemic model consisting five compartments within a total population with Crowley-Martin incidence rate and Holling type II \mbox{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. |
| Key words: epidemic model; Crowley-Martin incidence rate; extinction; persistence |