Dynamics of Age-Structure Smoking Models with Government Intervention Coverage under Fractal-Fractional Order Derivatives

Addai, Emmanuel; Adeniji, Adejimi A.; Peter, Olumuyiwa James; Agbaje, Janet O.; Oshinubi, Kayode

doi:10.3390/fractalfract7050370

Cited by 15 publications

(3 citation statements)

References 22 publications

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“…Over the years, mathematical modeling has played a major role in predicting incidence and mortality rates for infectious diseases such as COVID-19 [3]. Mathematical modeling has been shown to be a very effective technique for tracking and managing many diseases, such as tuberculosis, [4], malaria, and smoking-related diseases, suggesting possible government interventions [5,6]. Epidemiological and statistical modeling and analysis have been used for predicting incidence and mortality rates and to consider the impact that non-pharmaceutical intervention (NPI) control measures such as lockdowns, social distancing, and travel bans have had.…”

Section: Introductionmentioning

confidence: 99%

Modeling COVID-19 Disease with Deterministic and Data-Driven Models Using Daily Empirical Data in the United Kingdom

Agbaje,

Babasola,

Adeyemo

et al. 2024

COVID

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The COVID-19 pandemic has had a significant impact on countries worldwide, including the United Kingdom (UK). The UK has faced numerous challenges, but its response, including the rapid vaccination campaign, has been noteworthy. While progress has been made, the study of the pandemic is important to enable us to properly prepare for future epidemics. Collaboration, vigilance, and continued adherence to public health measures will be crucial in navigating the path to recovery and building resilience for the future. In this article, we propose an overview of the COVID-19 situation in the UK using both mathematical (a nonlinear differential equation model) and statistical (time series modeling on a moving window) models on the transmission dynamics of the COVID-19 virus from the beginning of the pandemic up until July 2022. This is achieved by integrating a hybrid model and daily empirical case and death data from the UK. We partition this dataset into before and after vaccination started in the UK to understand the influence of vaccination on disease dynamics. We used the mathematical model to present some mathematical analyses and the calculation of the basic reproduction number (R0). Following the sensitivity analysis index, we deduce that an increase in the rate of vaccination will decrease R0. Also, the model was fitted to the data from the UK to validate the mathematical model with real data, and we used the data to calculate time-varying R0. The homotopy perturbation method (HPM) was used for the numerical simulation to demonstrate the dynamics of the disease with varying parameters and the importance of vaccination. Furthermore, we used statistical modeling to validate our model by performing principal component analysis (PCA) to predict the evolution of the spread of the COVID-19 outbreak in the UK on some statistical predictor indicators from time series modeling on a 14-day moving window for detecting which of these indicators capture the dynamics of the disease spread across the epidemic curve. The results of the PCA, the index of dispersion, the fitted mathematical model, and the mathematical model simulation are all in agreement with the dynamics of the disease in the UK before and after vaccination started. Conclusively, our approach has been able to capture the dynamics of the pandemic at different phases of the disease outbreak, and the result presented will be useful to understand the evolution of the disease in the UK and future and emerging epidemics.

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Section: Introductionmentioning

confidence: 99%

Modeling COVID-19 Disease with Deterministic and Data-Driven Models Using Daily Empirical Data in the United Kingdom

Agbaje,

Babasola,

Adeyemo

et al. 2024

COVID

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“…One of the most promising areas of modern research is fractional calculus [24]. Numerous studies have been conducted in this field, which has resulted in amazing applications.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Tuberculosis Outbreak in an East African Country Incorporating Vaccination and Treatment

Oshinubi,

Peter,

Addai

et al. 2023

Computation

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In this paper, we develop a deterministic mathematical epidemic model for tuberculosis outbreaks in order to study the disease’s impact in a given population. We develop a qualitative analysis of the model by showing that the solution of the model is positive and bounded. The global stability analysis of the model uses Lyapunov functions and the threshold quantity of the model, which is the basic reproduction number is estimated. The existence and uniqueness analysis for Caputo fractional tuberculosis outbreak model is presented by transforming the deterministic model to a Caputo sense model. The deterministic model is used to predict real data from Uganda and Rwanda to see how well our model captured the dynamics of the disease in the countries considered. Furthermore, the sensitivity analysis of the parameters according to R0 was considered in this study. The normalised forward sensitivity index is used to determine the most sensitive variables that are important for infection control. We simulate the Caputo fractional tuberculosis outbreak model using the Adams–Bashforth–Moulton approach to investigate the impact of treatment and vaccine rates, as well as the disease trajectory. Overall, our findings imply that increasing vaccination and especially treatment availability for infected people can reduce the prevalence and burden of tuberculosis on the human population.

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“…Addai et al [16] presented a nonlinear fractional mathematical model for the smoke epidemic that includes two age groups using the Atangana-Baleanu-Caputo fractional derivative. More recently, Addai et al [17] studied the dynamics of the age-structure smoking model under fractal-fractional (F-F) derivatives with government intervention coverage in the Caputo-Fabrizio framework. Zeb et al [18] presented a four-class mathematical model-S (potential smokers), C (chain smokers), R (temporary quitters that can be movable to the relapse habit), and Q (permanent quitters of smoking)-in the form of fractional order.…”

Section: Introductionmentioning

confidence: 99%

Dynamic of Some Relapse in a Giving Up Smoking Model Described by Fractional Derivative

et al. 2023

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Smoking is associated with various detrimental health conditions, including cancer, heart disease, stroke, lung illnesses, diabetes, and fatal diseases. Motivated by the application of fractional calculus in epidemiological modeling and the exploration of memory and nonlocal effects, this paper introduces a mathematical model that captures the dynamics of relapse in a smoking cessation context and presents the dynamic behavior of the proposed model utilizing Caputo fractional derivatives. The model incorporates four compartments representing potential, persistent (heavy), temporally recovered, and permanently recovered smokers. The basic reproduction number R0 is computed, and the local and global dynamic behaviors of the free equilibrium smoking point (Y0) and the smoking-present equilibrium point (Y*) are analyzed. It is demonstrated that the free equilibrium smoking point (Y0) exhibits global asymptotic stability when R0≤1, while the smoking-present equilibrium point (Y*) is globally asymptotically stable when R0>1. Additionally, analytical results are validated through a numerical simulation using the predictor–corrector PECE method for fractional differential equations in Matlab software.

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Dynamics of Age-Structure Smoking Models with Government Intervention Coverage under Fractal-Fractional Order Derivatives

Cited by 15 publications

References 22 publications

Modeling COVID-19 Disease with Deterministic and Data-Driven Models Using Daily Empirical Data in the United Kingdom

Modeling COVID-19 Disease with Deterministic and Data-Driven Models Using Daily Empirical Data in the United Kingdom

Mathematical Modelling of Tuberculosis Outbreak in an East African Country Incorporating Vaccination and Treatment

Dynamic of Some Relapse in a Giving Up Smoking Model Described by Fractional Derivative

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