Browsing by Author "Zhang, Lingling"
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- ItemA fractional order age-specific smoke epidemic model(Elsevier, 2023) Addai, Emmanuel; Asamoah, Joshua Kiddy K.; Zhang, Lingling; Essel, John Fiifi; 0000-0002-7066-246XThis paper presents a nonlinear fractional mathematical model for the smoke epidemic that includes two age groups. To solve the smoke epidemic, the Atangana-Baleanu-Caputo fractional derivative is used. The Banach and Krasnoselskii type fixed point theorem is used to determine existence and uniqueness. We explored model stability using the Hyers-Ulam form of stability. Using Lagrange interpolation, the behaviour of the smoke epidemic of the 2-age group model is generated. The numerical simulation shows that the model has po- tential for both groups, and that age-specific interventions can be used to reduce smoking rates in the general population.
- ItemFractal-fractional order dynamics and numerical simulations of a Zika epidemic model with insecticide-treated nets(2022-06) Addai, Emmanuel; Zhang, Lingling; Ackora-Prah, Joseph; Gordon, Joseph Frank; Asamoah, Joshua Kiddy K.; Essel, John Fiifi; 0000-0002-7066-246XFractional order and fractal order are mathematical tools that can be used to model realworld problems. In order to demonstrate the usefulness of these operators, we develop a new fractal-fractional model for the propagation of the Zika virus. This model includes insecticide-treated nets and the generalized fractal-fractional Mittag-Leffler kernel. The existence, uniqueness, and Ulam–Hyres stability conditions for the given system are determined. Using the Newton polynomial, the numerical scheme is described. From the numerical simulations, we notice that a change in the fractal-fractional order directly affects the dynamics of the Zika virus. We also notice that the use of fractal order only converges to faster than the use of fractional order only. Testing the inherent potency of insecticide-treated nets when the fractal-fractional order is 0.99 indicates that increased use of insecticide-treated nets increases the number of healthy humans. The fractalfractional analysis captures the geometric pattern of the Zika virus that is repeated at every scale, which cannot be captured by classical geometry. This backs up the idea that the best way to control the disease is to know enough about how it spread in the past.
- ItemFractal–fractional age-structure study of omicron SARS-CoV-2 variant transmission dynamics(Elsevier, 2022-09) Addai, Emmanuel; Zhang, Lingling; Asamoah, Joshua Kiddy K.; Preko, Ama Kyerewaa; Arthur, Yarhands Dissou; 0000-0002-7066-246XThis paper proposes a new fractal–fractional age-structure model for the omicron SARS-CoV-2 variant under the Caputo–Fabrizio fractional order derivative. Caputo–Fabrizio fractal–fractional order is particularly successful in modelling real-world phenomena due to its repeated memory effect and ability to capture the exponentially decreasing impact of disease transmission dynamics. We consider two age groups, the first of which has a population under 50 and the second of a population beyond 50. Our results show that at a population dynamics level, there is a high infection and recovery of omicron SARS-CoV-2 variant infection among the population under 50 (Group-1), while a high infection rate and low recovery of omicron SARS-CoV-2 variant infection among the population beyond 50 (Group-2) when the fractal–fractional order is varied.
- ItemFractional order epidemiological model of SARS-CoV-2 dynamism involving Alzheimer’s disease(Elsevier, 2022-09) Addai, Emmanuel; Zhang, Lingling; Preko, Ama Kyerewaa; Asamoah, Joshua Kiddy K.; 0000-0002-7066-246XIn this paper, we study a Caputo–Fabrizio fractional order epidemiological model for the transmission dynamism of the severe acute respiratory syndrome coronavirus 2 pandemic and its relationship with Alzheimer’s disease. Alzheimer’s disease is incorporated into the model by evaluating its relevance to the quarantine strategy. We use functional techniques to demonstrate the proposed model stability under the Ulam–Hyres condition. The Adams–Bashforth method is used to determine the numerical solution for our proposed model. According to our numerical results, we notice that an increase in the quarantine parameter has minimal effect on the Alzheimer’s disease compartment.
- ItemFractional-Order Ebola-Malaria Coinfection Model with a Focus on Detection and Treatment Rate(Hindawi, 2022-09) Zhang, Lingling; Addai, Emmanuel; Ackora-Prah, Joseph; Dissou Arthur, Yarhands; Asamoah, Joshua Kiddy K.; 0000-0002-7066-246XCoinfection of Ebola virus and malaria is widespread, particularly in impoverished areas where malaria is already ubiquitous. Epidemics of Ebola virus disease arise on a sporadic basis in African nations with a high malaria burden. An observational study discovered that patients in Sierra Leone’s Ebola treatment centers were routinely infected with malaria parasites, increasing the risk of death. In this paper, we study Ebola-malaria coinfections under the generalized Mittag-Leffler kernel fractional derivative. The Banach fixed point theorem and the Krasnoselskii type are used to analyse the model’s existence and uniqueness. We discuss the model stability using the Hyers-Ulam functional analysis. The numerical scheme for the Ebolamalaria coinfections using Lagrange interpolation is presented. The numerical trajectories show that the prevalence of Ebolamalaria coinfections ranged from low to moderate depending on memory. This means that controlling the disease requires adequate knowledge of the past history of the dynamics of both malaria and Ebola. The graphical dynamics of the detection rate indicate that a variation in the detection rate only affects the following compartments: individuals that are latently infected with the Ebola, Ebola virus afflicted people who went unnoticed, individuals who have been infected with the Ebola virus and have been diagnosed with the disease, and persons undergoing Ebola virus therapy.