Infectious Disease Model With Pulse Vaccination

Pulse vaccination is an effective way to control the infectious diseases. Severalkinds of infectious disease models with pulse vaccination have been studied. Thedynamics behavior of models have been analyzed. Main research contents are asfollows：Firstly, the spread of some diseases depending on the infective with saturatedcontact rate is considered, so a kind of SIR epidemic model of pulse vaccination withsaturated contact rate and vertical transmission is built. By using the stroboscopicmap, the disease-free periodic solution of the model is got. By constructing Floquettheorem, the local stability of the infection-free periodic solution is proved. By usingimpulse differential inequality, the global stability of the disease-free periodicsolution is given. By using the comparison principle, the permanence condition ofthe model is obtained. Through the results of numerical simulation, the vaccinationrate is improved or disease recovery rate is increased, the disease can be reduce theprevalence.Secondly, on account of some disease have the latent period, delay has beenused to simulate latent phenomenon, so a kind of SIR epidemic model of pulsevaccination with discrete delay is built. By using the comparison principle, globalstability of the disease-free periodic solution and permanence condition of the modelare given. The impact of these parameters on the spread of disease is explainedtheoretically. By using numerical simulation, the connection between the latentperiod and vaccination cycle is got, the vaccination cycle is adjusted to the length oflatent period, the prevalence of disease could be avoided.Lastly, the lurker in latent period with continuous transmission characteristic isconsidered, a kind of SEIR epidemic model of pulse vaccination with saturatedcontact rate and distributed delay is built. By using the method of fixed pointprinciple, the global dynamic behavior of the model is got. By using the comparisonprinciple, global stability of the disease-free periodic solution and permanencecondition of the model are given. By using numerical simulation, the importance of the cure rate of the disease is proved. The cure rate is increased, the disease outbreakcould be controlled. Tuberculosis is applied to the model, the effectiveness of thecure rate is proved. By using the example to verify, the cure rate to eradicate thedisease is importance.