Stochastic modeling of the coronavirus disease 2019 with multiple infectious severities /
Muhammad Fahmi Bin Ahmad Zuber
- xiv, 142 pages : Illustration ; 30 cm.+ 1 CD-ROM.
Centre for Mathematical Sciences
Thesis (Doctor of Philosophy) -- Universiti Malaysia Pahang Al Sultan Abdullah – 2025
Includes bibliographical reference
The pandemic had a significant impact worldwide. We observe the shift of public and governmental concern regarding the pandemic as the pandemic continues. During the beginning of the pandemic, the concern is the need to understand the transmissibility of the disease. Later, as financial and social crises emerged, the concern shifted to the optimal non-pharmaceutical intervention (NPI) strictness and vaccination programs to effectively curb the pandemic transmission. Lastly, the concern shifted again to the severity of the pandemic, mainly toward the hospitalization, intensive care unit (ICU), and ventilation counts. To address the concern of higher severity cases, within the implementation of NPIs, we expand the “susceptible-infected-recovered-death” (SIRD) and developed a multiple severity of infected compartment model, the SInRD model. The characteristic of the model is investigated both theoretically (existence, uniqueness, boundedness, and positivity of solutions, equilibrium points and their stability, and basic reproduction number) and numerically (equilibrium points simulations and sensitivity of parameters towards compartments). The performance and application of the proposed model are investigated and proven reliable while providing the needed result of higher severity simulations. The model has a variable n as it could be adapted to the available number of infected compartments within the data. This allows for more accurate simulation and prediction of higher severity compartments, such as measuring the required hospital capacity or maintaining ventilation usage to a minimum. By providing detailed insights into disease severity progression, this model assists decision-makers in optimizing resource allocation and intervention strategies during critical pandemic phases. The automated workflow ensures rapid adaptability, enabling real-time policy adjustments based on the latest epidemiological data. To measure the spread of the pandemic, we utilize the parameter estimation algorithm, which is the MCMCstat toolbox library, specifically the Delayed Rejection Adaptive Metropolis (DRAM) thus estimating the required epidemiological parameters. In generalizing the algorithm, we developed several supplementary algorithms and calculated data-based prior values to support the toolbox to fit any pandemic data from any country, period, NPI implementations, and models we tested. For future numerical simulations, we utilized the estimated parameters alongside projections of the epidemiological parameters, using three numerical methods. The methods are fourth-order Runge-Kutta, Adam-Moulton Predictor Corrector, and fourth-order stochastic Runge-Kutta. All simulations shown within the thesis are made using the estimated epidemiological parameters and could be recreated within the GUI, alongside future predictions. Due to the high demand for simulation and results utilizing recent data, we designed the algorithm to automate processes from the obtained data to parameter estimation, numerical simulation, and GUI presentation, made to be almost autonomous. The pseudocodes are included explaining the process, and the sample code is in the appendix. In summary, the thesis contributes a workflow autonomously from data to results, utilizing a newly proposed compartmental model.
THE0010152 (Local)
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