Computational Study of Fractional-Order Vector Borne Diseases Model

Bedi, Pallavi; Khan, Aziz; Kumar, Anoop; Abdeljawad, Thabet

doi:10.1142/s0218348x22401491

Cited by 14 publications

(7 citation statements)

References 23 publications

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“…Tis proves that it is uniformly convergent (see [42]). Te limit of (16) as n ⟶ ∞ confrms the unique solution of these sequences and satisfes model (8). Tis guarantees the existence of a unique solution for model (8) according to (19).…”

Section: Existence and Uniqueness Resultsmentioning

confidence: 72%

“…It can also be used to understand the disease's mechanisms and identify potential targets for new therapies [5,6]. Many fractional diferential operators have been used in so-called mathematical epidemiology to model many infectious diseases as mathematical models of infectious diseases are important sources for understanding and interpreting the dynamics of those diseases such as coronaries, polycystic ovarian syndrome, tuberculosis, immunodefciency, infuenza, cancer, and hepatitis [7][8][9][10][11][12][13][14][15][16][17]. FDEs are crucial in understanding the dynamics of HIV/AIDS transmission.…”

Section: Introductionmentioning

confidence: 99%

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Conformable Fractional-Order Modeling and Analysis of HIV/AIDS Transmission Dynamics

Salah,

Sontakke,

Abdo

et al. 2024

International Journal of Differential Equations

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The mathematical model of the dynamics of HIV/AIDS infection transmission is developed by adding the set of infected but noninfectious persons, using a conformable fractional derivative in the Liouville–Caputo sense. Some fixed point theorems are applied to this model to investigate the existence and uniqueness of the solutions. It is determined what the system’s fundamental reproduction number R0 is. The disease-free equilibrium displays the model’s stability and the local stability around the equilibrium. The study also examined the effects of different biological features on the system through numerical simulations using the Adams–Moulton approach. Additionally, varied values of fractional orders are simulated numerically, demonstrating that the results generated by the conformable fractional derivative-based model are more physiologically plausible than integer-order derivatives.

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Section: Existence and Uniqueness Resultsmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Conformable Fractional-Order Modeling and Analysis of HIV/AIDS Transmission Dynamics

Salah,

Sontakke,

Abdo

et al. 2024

International Journal of Differential Equations

View full text Add to dashboard Cite

show abstract

“…Researchers can forecast a phenomenon's future by using mathematical models. For example, we can obtain a wealth of knowledge regarding the transmission dynamics, eradication, and future spread of infectious or viral diseases in society through the use of mathematical models and simulations of these diseases [9,10]. Recently, few mathematical models have been made in the area of coccidiosis.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies

Liana,

Swai

2024

Abstract and Applied Analysis

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Coccidiosis is an infectious disease caused by the Eimeria species. The species can infect a bird’s digestive system, severely slow down its growth, and is a serious economic burden for chickens. A mathematical model for the transmission dynamics of coccidiosis disease in chickens in the presence of control interventions has been formulated and analyzed to gain insights into the dynamics of the disease in the population. Three control interventions, namely vaccination, sanitation, and treatment, are implemented. The study intends to assess the effects of these control interventions in coccidiosis transmission dynamics. Using the theory of differential equations, the invariant set of the model was derived, and the model’s solution was found to be mathematically and biologically significant. Analytical methods are employed to establish equilibrium solutions and investigate the stability of the model system’s equilibria, while numerical simulations illustrate the analytical results. The effective reproduction number is obtained using the next-generation matrix method, and the local stability of the equilibria of the model is established. The disease-free equilibrium is proved to be locally stable when the effective reproduction number is less than unity. Also, the nature of the bifurcation and its implications for disease prevention are investigated through the application of the center manifold theory. On the other hand, sensitivity analysis is carried out to investigate the parameters that impact the transmission of coccidiosis disease using the normalized forward sensitivity index. The parameters that have a greater influence on the effective reproduction number should be targeted for control purposes to lessen the spread of disease. Furthermore, numerical simulation is performed to investigate the contribution of each control intervention.

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“…Tese vectors carry pathogenic organisms such as bacteria, viruses, fungi, protists, and parasitic worms which can be transferred from one host to another. Some examples of VBDs are dengue fever, Lyme disease, malaria, West Nile virus, Rift Valley fever, and Japanese encephalitis [1]. In many tropical and subtropical regions, malaria is a prevalent and potentially fatal infectious disease.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of an Age-Structured Malaria Model in the Sense of Atangana–Baleanu Fractional Operators

Menbiko,

Deressa

2024

Journal of Mathematics

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In this paper, integer- and fractional-order models are discussed to investigate the dynamics of malaria in a human host with a varied age distribution. A system of differential equation model with five human state variables and two mosquito state variables was examined. Preschool-age (0–5) and young-age individuals make up our model’s division of the human population. We investigated the existence of an area in which the model is both mathematically and epidemiologically well posed. According to the findings of our mathematical research, the disease-free equilibrium exists whenever the fundamental reproduction number R0 is smaller than one and is asymptotically stable. The disease-free equilibrium point is unstable when R0>1. We showed that the endemic equilibrium point is unique for R0>1. Also, the most influential control parameters of the spread of malaria were identified. Numerical simulations of both classical and fractional order were conducted, and we used ODE (45) for classical part and numerical technique developed by Toufik and Atangana for fractional order. The infected population will grow because of the high biting frequency of the mosquito and the high likelihood of transmission from the infected mosquito to the susceptible human. R=1.622, which is more than one, indicating that the mosquito vector keeps on growing. This supports the stability of the endemic equilibrium point theorem, which states that the disease becomes endemic when R=1. The susceptible human population will decrease because of the presence of the infective mosquito, which has a high biting frequency for the first couple of days. Since the infective mosquito bit the susceptible human, the susceptible human became infected and went to the infected human compartments. Then, the susceptible population will decrease and the infested human population will increase. After a certain amount of time, it becomes zero due to the growth of protected classes. In this case, a disease-free equilibrium point exists and is stable. This condition exists because R0=2.827×10−5 is less than 1. This supports the theorem that the stability of the disease-free equilibrium point is obtained when R0<1. Depending on equation, we have shown that the possibility of some endemic equilibria exists when R0<1, that is, it undergoes backward bifurcation, even when the disease-free equilibrium is locally stable, and the result means that the society may misunderstand the level of malaria prevalence in the community.

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Computational Study of Fractional-Order Vector Borne Diseases Model

Cited by 14 publications

References 23 publications

Conformable Fractional-Order Modeling and Analysis of HIV/AIDS Transmission Dynamics

Conformable Fractional-Order Modeling and Analysis of HIV/AIDS Transmission Dynamics

Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies

Modeling and Analysis of an Age-Structured Malaria Model in the Sense of Atangana–Baleanu Fractional Operators

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