Abstract
Inthispaper,anewSIRSepidemicmodelwhichconsiderstheinfluenceof
informationinterventionandenvironmentalnoiseisstudied.Thestudyshowsthat
informationinterventionandwhitenoisehavegreateffectsonthedisease.First,we
showthatthereisglobalexistenceandpositivityofthesolution.Then,weprovethat
thestochasticbasicproduction R
s
isathresholdwhichdeterminestheextinctionor
persistenceofthedisease.Whentheintensityofnoiseislarge,weobtain R
s
1anda
sufficientconditionfortheexistenceofstationarydistributionisobtained,which
meansthediseaseisprevalent.Finally,themainresultsareillustratedbynumerical
simulations.
Keywords: SIRSepidemicmodel;informationintervention;environmentalnoise;
stationarydistribution;extinction
1 Introduction
Itiswellknownthatdiseaseshaveagreateffectonpeople’shealth.Forexample,according
to thereport, theHN bird flu, which is the world’sfirst new subtype of influenza virus
withsymptomsoffeverandfeverintheearlydaysofthevirus,wasdiscoveredinShanghai
andAnhuiin.Untilnow,HNbirdfluhascausedmanyinfectionsordeaths.When
the infectious disease appears, how to prevent and treat disease is one of the hot issues
that people care about. Awareness is raised by increasing media coverage and health ed-
ucation, which can prevent or delay disease occurrence to a certain extent. For instance,
sincetheoutbreakoftheHNflu,thepublicmediahasbeenreportingthedailynumber
of infected people, the number of deaths, the symptoms and prevention measures of the
disease.Mediacoveragehasgreatlyreducedtherateofinfectionandhashadasignificant
impactondiseasecontrol.Fortreatmentofthedisease,inadditiontothedrugtreatment,
combining with non-drug therapy can be effective in half the effort, and psychotherapy
is a very effective method. A large number of studies have shown that many diseases are
relatedtoourthoughtsinvaryingdegrees[].Positivepsychologicalsuggestionwillmake
positive emotions generate, so as to avoid a negative effect of negative feelings caused by
negativeemotionsuggestiononthedisease,whichisofagreathelpincontrollingdisease
and restoring healthy life. Therefore, information intervention (media coverage, health
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BaoandZhangAdvancesinDifferenceEquations (2017) 2017:352 Page2of19
education,psychologicalsuggestion)asakindofnon-drugtreatmentisaveryimportant
methodforthepreventionandtreatmentofdiseases.
Currently, there have been many studies that considered taking information interven-
tion into series infectious diseases models including SIR, SEIR, SIRS, etc. For example,
Joshi et al. [] considered SIR infectious disease model which was based on information
intervention and found that information could reduce the level of infection. In addition,
Buonomoetal.[]studiedtheinfluenceofinformationonvaccinationatthetimeofnew
birth in an SEIR model, and he found that information induced vaccination may trigger
oscillationwhichisdifferentfromothers.Xiaoetal.[]foundthattheimpactoftheme-
diacouldnotonlydelaythepeakofdisease,butalsocouldreducetheseverity ofdisease
outbreak. In further work, Joshi et al. [] studied the effects of information or education
on the dynamic control of disease. Recently, Kumar et al. [] combined treatment and
information influence as control intervention, as well as put forward the following SIRS
epidemicmodel: