Please use this identifier to cite or link to this item: `http://prr.hec.gov.pk/jspui/handle/123456789/14874`
 Title: Mathematical modeling and analysis of hepatitis B Virus with Optimal control Authors: Ali Shah, Syed Azhar Keywords: Physical SciencesMathematics Issue Date: 2020 Publisher: University of Peshawar, Peshawar. Abstract: Mathematical modeling is very essential to express the phenomena and mechanism of an infectious disease, and to understand the dynamics of the infection. The proper treatment and suitable strategies are vital to managing the disaster of an infectious disease. In this dissertation, first we establish an integer-order-differential (IOD) model for hepatitis B virus (HBV) with treatment class to study the effect of treatment and biological parameters. We present a complete qualitative analysis of the proposed model, such as stability of equilibria, existence-uniqueness of presented model solution etc. Also we present the threshold quantity R0 of the model. Further, to overcome the burden of the HBV infection on the population, we incorporate the three time-dependent appropriate controlling variables in the IOD model to control and eradicate the HBV infection. To solve the IOD model with treatment class numerically, we use RK4 (Runge-Kutta order 4) technique. The numerical results illustrate the dynamics of HBV infection. Mathematical models with time-fractional order differential equations are more realistic and give comparatively better fit to the real data instead of IOD models. Moreover, due to its memory effect, it can be used successfully in modeling the phenomena of HBV. Therefore, in this dissertation, we extend the IOD model to time-fractional-order-differential model. We study the fractional operator with the help of Caputo-Fabrizio and Atangana-Baleanu in Caputo sense fractional order derivatives. Finally, the numerical simulations show that the model with fractional derivatives is biologically more feasible, reliable and the graphical results also show its usefulness. Gov't Doc #: 20211 URI: http://prr.hec.gov.pk/jspui/handle/123456789/14874 Appears in Collections: PhD Thesis of All Public / Private Sector Universities / DAIs.

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