| dc.description.abstract | Nowadays, with social and technological development, many kinds of infectious diseases have been under control in the mass by means of the high-tech and novel method in the use of medical research. Usually, besides the traditional ideas and approaches, the research based on dynamic mathematical modeling is becoming a significant tool to study infectious diseases. In addition, a feasible HIV or HBV dynamic mathematical model can facilitate us to find out a novel therapy and estimate/forecast the progress of drug resistance, side-effect or drug effect. In Chapter 3, an HIV mathematical model has considered some unknown parameters and unmeasurable CD8+T cell count. Then, a switching control strategy of drug treatment is proposed to suppress and sweep out the infected cells and the virus particles of blood plasma, and rebuild the immunologic homeostasis to increase the healthy cells. In terms of the Lyapunov function, the switching control corresponding to two different cases is designed to make the state variables of the HIV system approach the health equilibrium asymptotically without the influence of unknown parameters and unmeasurable cell counts. In Chapter 4, a more complicated HIV model is discussed and three types of control strategy for this model are designed. According to the Lyapunov function, this chapter synthesizes three theorems to as three types of control strategy for drug treatments u1(t) or/and u2(t), respectively, are designed to make all states converge to the infection-free equilibrium point of HIV model. In these three theorems, u1(t) or/and u2(t) can be a function of states or a fixed constant within a certain range. Similarly, in Chapter 5, antiviral therapy can usefully reduce the viral burden and switch off certain infectious sources for HBV-infected patients, and it has achieved several contributions and successes in disease control. In this chapter, an HBV mathematical model is considered. Three main theorems in which three different control strategies for drug treatments u1(t) or/and u2(t) are designed, respectively, to complete the final task of converging to the infection-free equilibrium point of HBV model asymptotically. Note that the designed drug treatments u1(t) or/and u2(t) are not a fixed value, but it is time-varying and dependent on states.
In conclusion, on the basis of Lyapunov function and nonlinear dynamic mathematical models of HIV and HBV, this dissertation proposes several methods to design controls for HIV and HBV models. Finally, several examples and simulation results are given to illustrate the availability, effectivity and accuracy of the proposed controls with different parameters in this dissertation.
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