|
| EFFECTS OF MEDIA COVERAGE AND TEMPORARY IMMUNITY TO A STOCHASTIC SEIR EPIDEMIC MODEL |
| Jing Zhang,Fengying Wei |
| (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, Fujian, PR China;Key Laboratory of Operations Research and Control of Universities in Fujian, Fuzhou University, Fuzhou 350116, Fujian, PR China) |
| DOI： |
| Abstract: |
| A type of SEIR epidemic model with media coverage and temporary
immunity is investigated in this paper. The existence and
uniqueness of the global positive solution with any positive
initial value is proved. Under the condition $R_0^s>1$, we prove
that the disease is persistent in the mean for a long run.
Furthermore, by constructing suitable Lyapunov functions, some
sufficient conditions that guarantee the existence of stationary
distribution are derived. We also obtain that, if the condition
$R_0^e<1$ is satisfied, then the disease is extinct with an
exponential rate. As a consequence, some examples and numerical
simulation are demonstrated to show the validity and feasibility
of the theoretical results. |
| Key words: stochastic SEIR model; media coverage; temporary immunity; persistence; extinction; stationary distribution |