article · Journal of the Nigerian Society of Physical Sciences
Mathematical modelling provides key insights into epidemic management by evaluating how immunisation drives alter disease trajectory. Focusing on the COVID-19 pandemic in Nigeria, a fractional-order mathematical model examines vaccination efficacy, minimum required effectiveness, and protection duration. Numerical solutions to the model are derived using the Laplace Adomian Decomposition Method, which relies on rapidly converging infinite series to track transmission dynamics. Simulations demonstrate the interaction between infection transmission rates and vaccination coverage. The analysis reveals that implementing a vaccination strategy in an integer order provides the most effective means of controlling viral transmission. These mathematical insights provide relevant evidence for public health planning, showing how analytical tools can clarify the dynamics of epidemic control and highlight the necessity of maximising immunisation coverage.
Understanding how vaccination rates and effectiveness shape disease transmission helps health authorities design better intervention programmes. By applying advanced mathematical techniques to Nigerian epidemic conditions, this work demonstrates how analytical models can quantify the protective impact of immunisation campaigns, offering healthcare workers and policymakers clear evidence to support resource planning and public health decisions during infectious disease outbreaks.
The work represents early-stage theoretical and computational modelling. It could inform decision-support software or analytical toolkits for public health planners, epidemiologists, and government agencies evaluating vaccination programmes. However, because the study is confined to mathematical simulation using the Laplace Adomian Decomposition Method, practical deployment would require translation into usable software tools and validation alongside operational public health data.
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This study underscores the crucial role of COVID-19 vaccinations in managing the pandemic, with a specific focus on Nigeria. Employing a fractional-order mathematical modeling approach, the research assesses vaccination efficacy, minimum effectiveness, and duration. The model’s numerical solution is derived through the Laplace Adomian Decomposition Method (LADM), utilizing rapidly converging infinite series. Simulation results illustrate the impact of COVID-19 transmission and vaccination rates. The study concludes that implementing a vaccination strategy in an integer order proves to be the most effective approach to controlling the spread of COVID-19. These findings have significant implications for researchers, policymakers, and healthcare workers. They emphasize the central role of fractional calculus in facilitating vaccine implementation in the ongoing battle against COVID-19. The study calls for global efforts to maximize vaccination implementation for the overall benefit of public health.
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DOI: 10.46481/jnsps.2024.1830
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