Systematic numerical algorithms and analysis of fractional order nonlinear delay epidemic systems.
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Date
2025-04-24
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UMT Lahore
Abstract
This research work is particularly concerned with the analysis of the behavior of infectious diseases and measures for their prevention. Diseases play a significant role in endangering human life, and mathematical modelling has emerged to be a very useful tool in managing disease outbreaks. In this context, we have transformed the integer-order models into a time-delayed fractional-order model by using the Caputo fractional differential operator and a delay factor. It offers a general solution at any time t and guarantees that all solutions are positive and bounded as expected in the real-world concerning disease transmission. The research investigates two key equilibrium states, disease-free equilibrium, which refers to the situation when the infection is not present in the population, and the endemic equilibrium, which implies the constant presence of the disease in the community. The quantity R0 is to assess the characteristics of outbreak, it is called the basic reproductive number. This is because the value of R0 is distinguishing in analyzing the stability of equilibria and outcome of the threat or control of the infection. A local and global stability analysis of dynamic model at both equilibrium states are carried out. For solving these delayed fractional-order model, a hybridized finite difference numerical method is proposed to get desired numerical solutions. This method makes it possible to simulate the behavior of the model with a high level of accuracy to identify the dynamics of the disease. The stability and structure of the numerical approach are discussed, and simulated figures are given to explain the biological characteristics of the model and the efficiency of the numerical technique. The results from these simulations are very useful in helping understand how disease control measures can be implemented and the effects of varying parameters based on the spread of the infection. This research can be very valuable in the study of infectious disease modeling as it gives a fresh perspective on how models can be made to be more satisfactory, useful, and helpful in the fight against diseases. Hence, the study goes ahead to establish the importance of R0 in disease control and establishes that fractional-order model analysis is a significant way of capturing the contagious disease transmission complexity. The conclusions made in this study provide a basis for further research on creating highly effective mathematical models for public health and epidemiology.
National significance/ linked sdgs
This research on "systematic numerical algorithms and fractional-order nonlinear delay epidemic systems" is of immense significance for Pakistan. The fundamental advantage of epidemic modeling with delay and fractional dynamics is that they provide efficient methods for modeling and predicting the spread of various infectious diseases, including dengue, hepatitis, and COVID-19, among other diseases. These diseases present multifaceted risks to the health of the Pakistani population, the country's economy, and the maintenance of society. It brings a new level of realism to policymaking and healthcare planning by employing more advanced numerical methods, allowing for more effective interventions, more efficient use of resources, and less strain on current healthcare infrastructure.
This research is relevant to "SDG 3: good health and well-being" since it relates to disease controlling and the improvement of healthcare systems with the help of modeling. It also contributes to "SDG 9: industry, innovation, and infrastructure" since proposals and subsequent advancements in computational and scientific investigations enhance Pakistan's capability in responding to multifaceted issues in the health sector. Additionally, it contributes to "SDG 4: quality education" by stimulating local scholars and scientists to investigate innovative technological fields.