Global Dynamics of Fractional-order Model for Malaria Disease Transmission

Helikumi, Mlyashimbi; Lolika, Paride O.

doi:10.9734/arjom/2022/v18i930409

Cited by 7 publications

(5 citation statements)

References 41 publications

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“…(See 58 ) Let g ( t ) be a function that satisfies some smoothness condition and , the derivative in Caputo form is define as: and for and . Also, the corresponding fractional integral is defined as …”

Section: Model Formulationmentioning

confidence: 99%

Modeling the dynamics of COVID-19 with real data from Thailand

Ibrahim

Humphries

Ngiamsunthorn

et al. 2023

Sci Rep

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In recent years, COVID-19 has evolved into many variants, posing new challenges for disease control and prevention. The Omicron variant, in particular, has been found to be highly contagious. In this study, we constructed and analyzed a mathematical model of COVID-19 transmission that incorporates vaccination and three different compartments of the infected population: asymptomatic $$(I_{a})$$ ( I a ) , symptomatic $$(I_{s})$$ ( I s ) , and Omicron $$(I_{m})$$ ( I m ) . The model is formulated in the Caputo sense, which allows for fractional derivatives that capture the memory effects of the disease dynamics. We proved the existence and uniqueness of the solution of the model, obtained the effective reproduction number, showed that the model exhibits both endemic and disease-free equilibrium points, and showed that backward bifurcation can occur. Furthermore, we documented the effects of asymptomatic infected individuals on the disease transmission. We validated the model using real data from Thailand and found that vaccination alone is insufficient to completely eradicate the disease. We also found that Thailand must monitor asymptomatic individuals through stringent testing to halt and subsequently eradicate the disease. Our study provides novel insights into the behavior and impact of the Omicron variant and suggests possible strategies to mitigate its spread.

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Section: Model Formulationmentioning

confidence: 99%

Modeling the dynamics of COVID-19 with real data from Thailand

Ibrahim

Humphries

Ngiamsunthorn

et al. 2023

Sci Rep

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“…The use of the reduced differential transform technique for two fractional-order cancer tumour models in the Caputo sense is discussed in [104]. To examine the consequences of heterogeneous vector biting exposure on the human population, researchers [105] developed and tested a fractional-order model for malaria disease transmission utilizing the Atangana-Baleanu derivative in Caputo sense. The nonlinear delayed Ross-Macdonald model for malaria transmission was generalized to a unique fractional-order model in [106], which improved the dynamics and added complexity.…”

Section: Contribution Of Fractional On Epidemic Modelmentioning

confidence: 99%

Untitled

2023

Progr. Fract. Differ. Appl.

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Both mathematics and science are important for one another and have a close relationship. It is impossible to dispute the significance of mathematics in a number of scientific disciplines, including electrical engineering, physics, biology, and medicine. Due to a number of applications of mathematical biology in the twenty-first century, researchers have taken a special interest in this field. Due to the complexity of the underlying connections, both deterministic and stochastic epidemiological models are founded on an inadequate understanding of the infectious network. Over the past several years, the use of different fractional operators to model the problem has grown, and it is now a common way to study how epidemics spread. New fractional operators, the infectious disease model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model's local and global stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical technique to obtain the solutions of the model and simulations. Also, we present conditions of existence for a solution to the purposed epidemic model and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. Infectious disease fractional order model is offered for analysis with simulations in order to determine the possible efficacy of disease transmission in the Community. The Fractal fractional operator is employed to study the dynamical transmission of diseases effect on society which is helpful for analysis, decision making, and disease control. Are treated with the Banach contraction principle. Microorganisms, interactions between individuals or groups, and environmental, social, economic, and demographic factors on a broader scale are all examples. Finally, numerical simulations that demonstrate the impact of fractional parameters on our found solutions are built to study the impact of the system parameter on the disease's spread. In conclusion, fractional operators in mathematical models can help decision-makers make better choices regarding the course of action to take in an epidemic situation. Further, we suggested some future work directions with the help of the new hybrid fractional operator. Fractional Calculus is a prominent topic for research within the discipline of Applied Mathematics due to its usefulness in solving problems in many different branches of science, engineering, and medicine. Recent researchers have identified the importance of mathematical tools in various disease models as being very useful to study the dynamics with the help of fractional and integer calculus modeling.

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“…Mathematical models have proved to be essential guiding tools for epidemiologists, biologists as well as policy makers (See for example [10,11,12,13,14,15,16,17,18]). Recently, modelling the transmission dynamics of brucellosis, is one of the most common global zoonoses [19], has been an interesting topic for a number of researchers (see, for example [6,18,20,21,22,23,24,25,26,27]).…”

Section: Introductionmentioning

confidence: 99%

“…The rationale of choosing the Caputo derivative is that the Caputo derivative for a given function which is constant is zero. Thus, the Caputo operator computes an ordinary differential equation, followed by a fractional integral to obtain the desired order of fractional derivative [11,28,31,32]. Most importantly, the Caputo fractional derivative allows the use of local initial conditions to be included in the derivation of the model [11,28,31,32].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Analysis of Chronic Brucellosis in Sheep

Lolika

Helikumi

2022

JAMCS

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We proposed and studied a new fractional-order model for the transmission dynamics of brucellosis with a special focus on the sheep-to-sheep transmission. Two control strategies namely; culling and vaccination rate are incorporated in the model. We computed the basic reproduction number R0 and we studied the global stability of disease-free and endemic equilibrium point in terms of basic reproduction number R0: We found that both the disease-free and endemic equilibrium points are globally stable whenever R0 < 1 and R0 > 1 respectively. In numerical simulations, we performed the sensitivity analysis of the model and expressed the relationship between model parameters and R0:We noted that, increase on the magnitude of model parameters with negative correlation coefficients would significantly reduce the spread of Brucellosis disease in the population. Moreover, model validation and parameter estimation for fractional-order and classical integer-order derivatives was carried out using real brucellosis for Egypt, 1999-2011. Overall, we noted that fractional-order model gave better prediction of brucellosis compared to classical integer-order model. Furthermore, we investigated the role of memory effects on the transmission of brucellosis in the population. We observe that, the memory effects have influenceon the transmission of brucellosis in the community. In addition, we noted that the aforementioned control strategies have the potential to reduce the transmission of brucellosis in the population. In particular, we observed that whenever the culling and vaccination rate is greater than 40% and 50% respectively, the disease dies out in the population.

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Global Dynamics of Fractional-order Model for Malaria Disease Transmission

Cited by 7 publications

References 41 publications

Modeling the dynamics of COVID-19 with real data from Thailand

Modeling the dynamics of COVID-19 with real data from Thailand

Untitled

Dynamics and Analysis of Chronic Brucellosis in Sheep

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