M.Phil / MS

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Numerical Approximation for the Solution of COVID-19 Pandemic Model
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Fariha Nawaz; FA19-RMT-106; Dr. Sadia Arshad; LHR TP 7393
Many mathematical models give different strategy for controlling speciﬁc diseases. The method of constructing a mathematical model is known as mathematical modelling. Fin- ishing the global disease lacks the use of different measures, such as civil separation, inter- action, and screening. we construct various models to predict the progression of COVID- 19 infection using data from Tunisia and Wuhan in fractional order ν. This epidemiologic analysis model suggests how we may predict the spread of COVID-19 by applying the basic reproduction number R0. The susceptibility of threshold number R0 regarding the frame- work of the epidemic model. R0 can be calculated from different approximative methods in COVID-19 epidemic models. The global elements of equilibria, positivity, boundedness, and stability analysis are all given particular attention. For stability if R0 < 1, an infected person transfer the disease individually in new infected is less than one on average over the lifetime of its infectious time, and the infection cannot spread, while R0 > 1 then disease transfer from each infected person to more than one new infection on average and system will unstable. Using Adams-Bashforth-Moulton method, we get numerical result of the proposed model. In graphical work, we compare actual results with approximate solutions.
Modelling And Analysis Of The Outbreak Of COVID-19
(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Waseem Shokat; FA19-RMT-009; LHR TP 7433; Dr. Sadia Arshad
Mathematical models provide different strategies to control different diseases. The way toward building up a mathematical model is named mathematical Modelling. We develop different models that estimate the course of infection COVID-19 to help through a viable control system and effectiveness of vaccine by using data of Saudia Arabia, Italy, Canada and Pakistan via fractional order q. These model of epidemiologic analysis to predict that how COVID-19 spread and how we can control outbreak of this virus by using basic reproduction number R0. Special consideration is given to the worldwide elements of the equilibria, positiveness, boundedness and stability analysis. For stability if R0 < 1, an infected person transfer the disease individually in new infected is less than one on average over the lifetime of its infectious time, and the infection cannot spread. On the other hand at endemic equilibrium point if R0 > 1, then disease transfer from each infected person to more than one new infection on average and the disease will spread across the population. Sensitivity of models will be studied in different variations of parameters, focusing in particular on parameters that may arise. Moreover, the fitting of parameters through least squares curve fitting technique is performed. Finishing the worldwide disease lacks usage of various precaution, counting civil Separating, contact, testing following and more people should be vaccinated.
Construction of Numerical Approximation for Solving Fractional Partial Differential Equations
(Library Information Services COMSATS University Islamabad Lahore Campus, 2020) Bushra Nisar; FA19-RMT-024; LHR TP 7354; Dr. Sadia Arshad
In this thesis we have solve fractional-partial-differential(FPD) equations. In Chapter 2 for nonlinear time-space fractional Schr¨odinger(TSFS) equation an implicit finite difference (IFD) scheme is developed which is unconditionally-stable at order O(t2􀀀b + ¯h2) where t is time and ¯h is space step-size. Computational cost is lower for non-linear part by developing the explicit implicit scheme (EIS). And for the coupled TSFS system IFD scheme is developed which is also unconditionally-stable. The efficiency and accuracy of developed schemes are verified by numerical experiments. In Chapter 3 one step exponential time differencing (ETD) in temporal and two step ETD and in spatial fractional centered-difference scheme(CDS) are applied to solve the semilinear TSFS equation. Effectiveness of the numerical method is enhanced by two parametric mittag-leffler-function(MLF) which is evaluated by Pad ´ e-approximations. Effectiveness of the develop scheme is given by several examples. In Chapter 4 nonlinear TSFS equation is resolved by a Crank Nicolson-difference(CND) method. Stability and truncation-error of method are described. For improving the effectiveness of calculation a three level Linearized-difference-method (LDM) is also developed. In Chapter 5 a compact finite difference numerical scheme is developed for time fractional fourth order diffusion equation. In this paper spatial domain is discretized by Stepenhnson’s scheme and for time derivative fractional trapezoid formula is used. There is also presented complete stability and convergence analysis at the order of O(t2 +h4). The accuracy and effectiveness of proposed scheme is analyzed by numerical experiments showing that our numerical experiments are agreed with our analytical results.

M.Phil / MS

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