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 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.