Modeling the booster vaccine effect on new COVID-19 variant management employs the Atangana-Baleanu-Caputo fractional derivative operator together with the Laplace-Adomian decomposition method

Abstract

Introduction

New COVID-19 variants create worldwide health difficulties that call for effective control methods including booster vaccinations. The risk factors associated with new COVID-19 variants include enhanced transmission capabilities together with escape from immune responses and more severe disease manifestations which requires advanced vaccination measures. The developed mathematical model assesses how effectively booster vaccines help stop new COVID-19 variants from transmitting between people. Environmental variables that measure both public vaccine acceptance levels and widespread awareness levels integrated with the model to determine their roles in disease propagation rates. The research introduces fractional calculus to examine disease progress as well as booster vaccination effectiveness in stopping outbreaks.

Methods

This research establishes a fractional mathematical model to evaluate how booster vaccinations affect the spread of new COVID-19 variants. The stability evaluations and determination of basic reproduction number (R0) through next-generation matrix method form the basis of operational analysis for the model. Sensitivity analysis evaluates the effects that variable modifications have on disease outbreak controls. Evaluating complex fractional differential equations requires the analytical solutions derived by employing the Laplace-Adomian Decomposition Method (LADM). The solution approach provides accurate insights into equilibrium points as well as stability patterns together with control measures of disease transmission through vaccination strategies.

Results

Numerical data confirms the success of booster vaccination strategies because they lower transmission rates of infections and manage disease spread. Boosted vaccination rates lead to substantial decline in the basic reproduction number (R0) thus reducing disease transmission across the population. Sensitivity analysis shows how vaccine acceptance together with public awareness directly affects the maximum results achievable through booster doses. Success rates of vaccination programs heavily depend on behavioral elements which include vaccine hesitancy together with social perceptions about immunizations. The study demonstrates how vaccinating people alongside education programs leads to superior transmission control which supports long-lasting mitigation tactics.

Conclusion

The research evidence shows that booster vaccinations play a critical role in containing new COVID-19 variant spread. The research enables a full disease dynamics understanding through its integrated fractional-order model with behavioral components so it delivers effective vaccination optimization recommendations. Public health measures together with transmission control improve when people become more aware of vaccines. This developed model provides both scientific fundamentals for behavioral approaches in disease modeling and operational guidance to policy makers who need to create efficient vaccination programs. Booster vaccinations used together with awareness-raising programs establish a strong framework to manage the impact of new COVID-19 variants along with other infectious diseases.