A fractional order vaccination model for COVID-19 incorporating environmental transmission: a case study using Nigerian data

Atede, Anne Ojoma; Omame, Andrew; Inyama, S. C.

doi:10.59292/bulletinbiomath.2023005

Cited by 19 publications

(10 citation statements)

References 28 publications

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“…The field of epidemiology heavily relies on nonlinear models [8][9][10][11] to describe the dynamics of lethal COVID-19 transmission. These simulations are beneficial for societal planners and decision-makers in the health sector.…”

Section: Model Formulationmentioning

confidence: 99%

Modeling and investigating the spread of COVID-19 dynamics with Atangana-Baleanu fractional derivative: a numerical prospective

Raza,

Asad Ullah

et al. 2024

Phys. Scr.

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Fractional-order models have been used in the study of COVID-19 to incorporate memory and hereditary properties into the systems. These models have been applied to analyze the dynamics and behavior of the novel coronavirus. Various fractional-order models have been proposed, including the SIR and SEIR models, with the addition of compartments such as asymptomatic classes and virus repositories. Overall, fractional-order models have proven to be effective in studying the dynamics and spread of COVID-19. In this paper, we propose a nonlinear fractional model employing the Atangana-Baleanu derivative to describe COVID-19. To offer a clearer perspective, our investigation incorporates two distinct quarantine stages within the population. The first quarantine class consists of individuals who have not yet contracted the virus but have chosen to self-isolate at home. The second quarantine class encompasses individuals who are infected and are undergoing quarantine in hospitals. Additionally, we introduce a vaccination class, consisting of the portion of the population that has received the COVID-19 vaccination and is now at a reduced risk of infection. Fixed point theorems are employed to prove the existence and uniqueness of the solutions. The model's threshold parameter Ro is calculated to investigate the pandemic's future dynamics. The Toufik-Atangana scheme is applied to obtain numerical solutions for the fractional model. Further, we analyzed the data to assess how vaccination impacts the spread of the virus.The model includes two novel parameters to determine the speed and effectiveness of vaccination measures. To evaluate the accuracy of our model, we simulate the graphical results of this stage and compared them with integer-order derivative. The mathematical model for COVID-19 shows that both equilibrium points are locally stable. Moreover, to gain a deeper understanding of the disease, we conduct a sensitivity analysis to examine the effect of parameters on Ro.

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Section: Model Formulationmentioning

confidence: 99%

Modeling and investigating the spread of COVID-19 dynamics with Atangana-Baleanu fractional derivative: a numerical prospective

Raza,

Asad Ullah

et al. 2024

Phys. Scr.

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“…This might contribute to the development of treatments for HIV-1 and HTLV-1 with the potential to boost HIV-1-specific antibody and HTLV-1-specific CTL responses. There are other methods to expand our proposed model, such by integrating: (i) reaction diffusion [42], (ii) memory effect [43,44], (iii) stochastic effect [44,45] and (iv) time delay [8,40]. Future studies might also focus on including the effects of vaccines and antiviral drugs into the model.…”

Section: Impact Of Ctl and Antibody Responses On The System's Behaviormentioning

confidence: 99%

Dynamics of HIV-1 and HTLV-1 Coinfection with both CTL and Antibody Responses

Elaiw,

AlShamrani,

AlSulami

et al. 2024

Contemp. Math.

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Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type 1 (HTLV-1) coinfection models with simply an antibody response or a CTL response have been the subject of several recent investigations. Thus, the primary objective of this paper is to formulate and examine a mathematical framework for analyzing the intricate dynamics of coinfection between HIV-1 and HTLV-1. The model takes into account the role of antibody response against free HIV-1 particles and CTL response against HTLV-1-infected cells. We prove that the model is well-posed and it admits eight equilibria. The stability and existence of the equilibria are precisely controlled by eight threshold parameters ℜi, i = 1, 2, ..., 8. By formulating suitable Lyapunov functions and applying LaSalle's invariance principle, we show the global asymptotic stability for all equilibria. To demonstrate the theoretical results, we conduct numerical simulations. We look at how the antibody and CTL responses affect the dynamical behavior of HIV-1/HTLV-1 coinfection. Although the parameters of antibody and CTL responses have no effect on the basic reproduction ratio of HIV-1 single-infection (ℜ₁) and HTLV-1 single-infection (ℜ₂), it has been demonstrated that viral coinfection can be inhibited by immunological activation of antibody and CTL responses. This could potentially facilitate the advancement of therapeutic approaches for HIV-1 and HTLV-1, which have the capability to enhance the HIV-1-specific antibody and HTLV-1-specific CTL reactions.

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“…For instance, several mathematical models of COVID-19 have been carried out to understand the transmission patterns [7][8][9][10][11][12][13][14][15]. The impact of the environment on the transmission dynamics of COVID-19 patterns has been studied in the given literature [16,17]. The impact of quarantine and social distancing on the transmission dynamics of COVID-19 is explored in the given literature [18,19].…”

Section: Introductionmentioning

confidence: 99%

Mechanistic insights of COVID-19 dynamics by considering the influence of neurodegeneration and memory trace

Joshi

2024

Phys. Scr.

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COVID-19 has been declared a global pandemic as it disturbs education, society, agriculture, the economy, poverty, death rate, social development, mental psychology, and many more. Neurodegenerative disease is a brain disorder associated with several pathological factors along with mental psychology. This paper introduces a mathematical model to inspect mechanistic insights into COVID-19 dynamics by considering the influence of neurodegeneration and memory trace. The analysis of the proposed model and the existence and uniqueness of the model are derived using the ﬁxed-point criteria. A numerical experiment is presented to validate the theoretical results and examine the impact of various biological parameters, the influence of neurodegeneration, and memory trace on the transmission dynamics of COVID-19.

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A fractional order vaccination model for COVID-19 incorporating environmental transmission: a case study using Nigerian data

Cited by 19 publications

References 28 publications

Modeling and investigating the spread of COVID-19 dynamics with Atangana-Baleanu fractional derivative: a numerical prospective

Modeling and investigating the spread of COVID-19 dynamics with Atangana-Baleanu fractional derivative: a numerical prospective

Dynamics of HIV-1 and HTLV-1 Coinfection with both CTL and Antibody Responses

Mechanistic insights of COVID-19 dynamics by considering the influence of neurodegeneration and memory trace

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