Mathematical modelling of covid-19 transmission and vaccine effectiveness for a university / Shahirah Atikah Binti Mohamad Husnin

Centre for Mathematical Sciences

Thesis (Master of Science (Mathematics)) -- Universiti Malaysia Pahang – 2024

Includes bibliographical references

Due to the ongoing Coronavirus Disease 2019 (COVID-19) endemic, proper mathematical modelling to capture disease transmission is an essential tool for developing control methods and identifying driving factors in disease dynamics. However, COVID-19 modelling is not a one-size-fits-all approach, as it varies depending on many factors such as vaccination, intervention measures, social distancing and population. In this study, an improved mathematical model was proposed with time-dependent epidemiological parameters for COVID-19 by considering the factors of lockdown and vaccination for a university in Malaysia. The model is based on Susceptible-Infected-Recovered-Dead (SIRD) framework and in the form of a set of Ordinary Differential Equations. The model development involved three stages. It begins with the simplest setting of the model which used constant epidemiological parameters known as Model I that neglect the vaccination factor. Then, the model's complexity was increased to Model II, utilizing the time-dependent epidemiological parameters. The final stage is Model III which used time-dependent epidemiological parameters and included the vaccination factor. The models were numerically solved using the Runge Kutta fourth order method (RK4) and parameter fitting techniques namely Pattern Search and Nelder-Mead Simplex algorithm embedded in MATLAB software. In addition, a sensitivity analysis of the parameters was carried out to determine the relative influence of the model parameters on disease transmissions. To validate the results, a comparison between the model and the actual data was carried out and measured using mean absolute percentage error (MAPE) and root mean squared error (RMSE). As a result, Model III was adequately fitted to the actual data. In addition, a MATLAB-based graphical user interface (GUI) was developed to provide a better insight to the effectiveness of the vaccine in a population. The GUI is able to provide a rough percentage of vaccine effectiveness, as indicated by the good agreement of the projection and the actual data for the university. This research offers healthcare personnel a validated mathematical model along with tools for analysis and visualization which enables to make data-driven decisions and effectively manage the impact of COVID-19 within the university population. In future work, the developed mathematical model can be extended to incorporate the diversity of available vaccines, considering their varying efficacies and mechanisms of action.