Dynamics Of Epidemic Model With Limited Medical Resources

The main purpose of this thesis is to explore how the limited medical resourcesafect the transmission of infectious diseases, and analyze control strategies withthe limited medical resources.In frst chapter, we review some propaedeutic about epidemic dynamics, andintroduce main jobs in this thesis.In second chapter, dynamics of an SIR epidemic model is explored in order tounderstand how the limited medical resources and their supply efciency afect thetransmission of infectious diseases. The study reveals that, with varying amountof medical resources and their supply efciency, the target model admits bothbackward bifurcation and Hopf bifurcation. Sufcient criteria are established forthe existence of backward bifurcation, the existence, the stability and the directionof Hopf bifurcation. The mechanism of backward bifurcation and its implicationfor the control of the infectious disease are also explored. Numerical simulationsare presented to support and complement the theoretical fndings.In third chapter, a multigroup SIR epidemiological model is used to study theefects of group-targeted vaccination strategies on disease control and prevention.The model takes into consideration both proportionate and preferential mixingpatterns between groups. We show that the dynamical behaviors of the model aredetermined by the control reproduction number Rvand, under certain conditions,by the type-reproduction number T1v. These reproduction numbers provide criteriafor evaluating control strategies including targeted vaccination programs and re-duction of interactions between groups. We also illustrate how these reproductionnumbers can be used to examine the influence of population heterogeneities suchas group preferences, activity levels, and mixing patterns. Criteria are also estab-lished for disease eradication from the entire network of populations by applyingvaccination strategies in one or some sub-populations. In fourth chapter, we formulate an epidemic model with both human andsheep stock are considered to study the trend, critical factors and optimal controlstrategies of brucellosis in inner Mongolia. Based on multi-objective optimizationtheory, optimal control theory and Pontryagin’s maximum principle, we obtainoptimal strategies of vaccinating susceptible sheep and prevention education tominimize the total loss. Non-linear least-square estimation and sensitivity analysisare carried out for critical parameters. At last, we also give simulations of thedisease’s transmission and the numerical solutions of the optimal controls. Ourfndings reveal that the current control strategy can not eliminate the disease, andwe should also enhance the culling of infected sheep and keep the sheep populationsize at a right quantity.