Dynamical Analysis of the Epidemic Models of COVID-19 and Influenza

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