Abstract:
This thesis presents mathematical models that accurately depict the dynamics of both
COVID-19 and influenza epidemics. The COVID-19 model incorporates the Caputo fractional
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
