Dynamics Analysis Of Epidemic With Staged Progression On Complex Networks

In the39kinds of epidemics which request reporting according to the stipulation of“Infectious Disease Prevention Law”, the character of staged progression clinically appearsin almost65%epidemics. The infection and spread features vary along with time. It iscommon to see that the outbreak of epidemic with staged progression features, such asrabies, measles and syphilis. However, the stage character was ignored by the formerresearches. In addition to, the heterogeneity of contact methods to different individualsignored neither. The assumption of homogeneous mixing has become an obstacle to limitthe development of research. Fortunately, the diversity of contact methods to differentindividuals can be represented by complex networks. Therefore, it is necessary to considerboth characters above to solve practical issue. The mathematical theory analysis and proofare absent in some literature which combined the multi-infectious period and complexnetworks. In this paper, we divide individuals into more classes, consider the heterogeneityof contact methods and make mathematical analysis of model. The detail researches asfollowing:1. Considering a staged progression SIR epidemic model on complex networks.Withthe analysis of dynamical behavior, the basic reproduction number and final size areobtained. The heterogeneous networks structure and early stage patients can intensify thedisease spreading. Then, the final size is affected by transmission rate, recovery rate, initialvalues of infected and topology of network.2. Considering a multi-staged progression SIS epidemic model on complex networks,which can be used to represent arbitrarily distributed infectious period.By usingmathematical analysis, the basic reproduction number for the model is derived. The global dynamics are completely determined byR0: ifR01,the disease-free equilibrium of themodel is globally asymptotically stable, then the disease dies out; ifR01,then the diseasepersists in the crowd and there exists an unique endemic equilibrium such that it is globallyasymptotically attractive.3. Considering an epidemic spread and control model with arbitrarily distributedinfectious period on complex networks. Both targeted and uniform immunizations cancontrol the prevalence of epidemic. Moreover, the difference between different infectiousperiods produces no effects on the performance of targeted immunization.