M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item 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 7393Many 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.Item 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 ArshadMathematical 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.Item 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 ArshadIn 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(t2b + ¯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.Item Dynamical Analysis of the Epidemic Models of COVID-19 and Influenza(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Hamza Shafiq; FA21-RMT-015; Dr. Sadia Arshad; LHR TP 8709This thesis presents mathematical models that accurately depict the dynamics of both COVID-19 and influenza epidemics. The COVID-19 model incorporates the Caputo frac tional derivative, resulting in a system characterized by the variables(Sp,Qp,Ep,Ap,Ip,Dp,Rp,Vp). The stability of the steady state is evaluated by examining qualitative characteristics and the R0 coefficient. Furthermore, a demonstration is shown to prove the presence, limitedness, and positivity of a solution. A comprehensive examination is performed on the impacts of quarantine restrictions, and the stability of equilibrium points is investigated using fixed point theory. The fractional Trapezoidal approach is used for approximating solutions of the model. Two mathematical models were constructed to examine the dynamics of epidemics and different subtypes of influenza in Hong Kong between 2017 and 2018. These models used fundamental ordinary differential equations (ODEs). The parameterization method uses weekly data from the Hong Kong Centre of Health Protection. According to the study, just 11.6% of people received the influenza vaccine during the winter of 2017-2018, far below the required 72% needed to achieve herd immunity. This research emphasizes the challenge of achieving a harmonious equilibrium between the effectiveness of vaccinations and achieving the required level of immunization coverage. Additionally, it implies that there might be consequences for the incidence of specific subcategories of influenza.