A Reliable Stochastic Numerical Analysis for Typhoid Fever Incorporating With Protection Against Infection

Arif, Muhammad; Raza, Ali; Rafiq, Muhammad; Bibi, Mairaj; Fayyaz, Rabia; Naz, Mehvish; Javed, Umar

doi:10.32604/cmc.2019.04655

Cited by 24 publications

(5 citation statements)

References 20 publications

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“…We examined the mathematical model previously discussed by Arif et al 2 Here, represents the proportion of humans who are protected, represents the proportion of humans who are susceptible, signifies the fraction of humans who are currently infected, and indicates the fraction of humans receiving treatment. The rate at which humans receiving treatment transitions from the fraction of infected humans is denoted as .…”

Section: Typhoid Fever Model With Fuzzy Parametersmentioning

confidence: 99%

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Numerical investigation of a typhoid disease model in fuzzy environment

Dayan,

Ahmed,

Ali

et al. 2023

Sci Rep

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Salmonella Typhi, a bacteria, is responsible for typhoid fever, a potentially dangerous infection. Typhoid fever affects a large number of people each year, estimated to be between 11 and 20 million, resulting in a high mortality rate of 128,000 to 161,000 deaths. This research investigates a robust numerical analytic strategy for typhoid fever that takes infection protection into consideration and incorporates fuzzy parameters. The use of fuzzy parameters acknowledges the variation in parameter values among individuals in the population, which leads to uncertainties. Because of their diverse histories, different age groups within this community may exhibit distinct customs, habits, and levels of resistance. Fuzzy theory appears as the most appropriate instrument for dealing with these uncertainty. With this in mind, a model of typhoid fever featuring fuzzy parameters is thoroughly examined. Two numerical techniques are developed within a fuzzy framework to address this model. We employ the non-standard finite difference (NSFD) scheme, which ensures the preservation of essential properties like dynamic consistency and positivity. Additionally, we conduct numerical simulations to illustrate the practical applicability of the developed technique. In contrast to many classical methods commonly found in the literature, the proposed approach exhibits unconditional convergence, solidifying its status as a dependable tool for investigating the dynamics of typhoid disease.

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Section: Typhoid Fever Model With Fuzzy Parametersmentioning

confidence: 99%

“…Typhoid is currently treated with oral and injectable vaccines, however, these two are insufficient to eradicate the illness. The length of the sickness can be shortened if a drug-resistant strain is used to treat the infected person 1 , 2 .…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of a typhoid disease model in fuzzy environment

Dayan,

Ahmed,

Ali

et al. 2023

Sci Rep

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“…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. A stochastic model for co-infection with pneumonia and typhoid was published in [107] to examine the varied connections between the two diseases under the effect of preventative measures that consider environmental noise and piecewise fractional derivative operators, as well as some applications in [108]. A compartmental model for the transmission of dengue fever with nonlinear forces of infection via fractional derivative was created in citation 130.…”

Section: Contribution Of Fractional On Epidemic Modelmentioning

confidence: 99%

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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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“…Shoaib Arif et al presented a stochastic model of COVID-19 and studied it using NSFD scheme [26]. Researchers studied fractional stochastic models, for example [27], for example. Naveed et al studied a COVID-19 model with delay effect using NSFD theory [28].…”

Section: Introductionmentioning

confidence: 99%

Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

Băleanu¹,

Dayan²,

Ahmed³

et al. 2023

Computers, Materials &Amp; Continua

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The first major outbreak of the severely complicated hand, foot and mouth disease (HFMD), primarily caused by enterovirus 71, was reported in Taiwan in 1998. HFMD surveillance is needed to assess the spread of HFMD. The parameters we use in mathematical models are usually classical mathematical parameters, called crisp parameters, which are taken for granted. But any biological or physical phenomenon is best explained by uncertainty. To represent a realistic situation in any mathematical model, fuzzy parameters can be very useful. Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling. However, few works use fuzzy theory in building models to simulate HFMD dynamics. In this context, we examined an HFMD model with fuzzy parameters. A Non Standard Finite Difference (NSFD) scheme is developed to solve the model. The developed technique retains essential properties such as positivity and dynamic consistency. Numerical simulations are presented to support the analytical results. The convergence and consistency of the proposed method are also discussed. The proposed method converges unconditionally while the many classical methods in the literature do not possess this property. In this regard, our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.

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A Reliable Stochastic Numerical Analysis for Typhoid Fever Incorporating With Protection Against Infection

Cited by 24 publications

References 20 publications

Numerical investigation of a typhoid disease model in fuzzy environment

Numerical investigation of a typhoid disease model in fuzzy environment

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Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

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