An Atangana–Baleanu derivative-based fractal-fractional order model for the monkey pox virus: A case study of USA

Partial Differential Equations in Applied Mathematics, Journal Year: 2024, Volume and Issue: 9, P. 100623 - 100623

Published: Jan. 23, 2024

In this study, we apply both classical and fractional-order differential equations to construct a deterministic mathematical model of the monkeypox virus. The accounts for every conceivable interaction that may play role in propagation disease throughout population. current investigate outbreak using an Atangana-Beleanu fractal-fractional derivative with exponentially decaying type kernel examine impact vaccination isolation. We thoroughly model's fundamental characteristics. calculate basic reproduction number equilibrium points, as well identify feasible region model. prove existence stability Banach fixed-point theory Picard's successive approximation method. establish uniqueness solution under appropriate conditions. Additionally, explore asymptotically local global disease-free states endemic states. also Hyers-Ulam Hyers-Ulam-Rassias consistency obsessive solution. To design effective infection control measures, study dynamic behavior system. complex dynamics influence different system input factors through extensive numerical simulations proposed varying parameters. way, people can learn about parameters efforts eradicate monkeypox. dynamical present decision-makers community

Language: Английский

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Dynamics of the optimality control of transmission of infectious disease: a sensitivity analysis

Scientific Reports, Journal Year: 2024, Volume and Issue: 14(1)

Published: Jan. 10, 2024

Abstract Over the course of history global population has witnessed deterioration unprecedented scale caused by infectious transmission. The necessity to mitigate flow requires launch a well-directed and inclusive set efforts. Motivated urge for continuous improvement in existing schemes, this article aims at encapsulation dynamics spread diseases. objectives are served disease model. Moreover, an optimal control strategy is introduced ensure incorporation most feasible health interventions reduce number infected individuals. outcomes research facilitated stratifying into five compartments that susceptible class, acute chronic recovered vaccinated class. formulated incorporating specific variables namely, awareness about medication, isolation, ventilation, vaccination rates, quarantine level. developed model validated proving pivotal delicacies such as positivity, invariant region, reproduction number, stability, sensitivity analysis. legitimacy proposed delineated through detailed analysis along with documentation local features comprehensive manner. maximum index parameters transmission people moved from stages whose value (0.439, 1) increase parameter 10 percent would threshold quantity (4.39, 1). Under condition stable system, we inverse relationship between class time. assist gain fundamental aim research, take time-dependent obtain minimize populations maximize population, simultaneously. attained employment Pontryagin principle. Furthermore, efficacy usual quarantine, face mask usage, hand sanitation also noticed. effectiveness suggested plan explained using numerical evaluation. advantages new highlighted article.

Language: Английский

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An optimal control model for dengue dynamics with asymptomatic, isolation, and vigilant compartments

Decision Analytics Journal, Journal Year: 2024, Volume and Issue: 10, P. 100413 - 100413

Published: Feb. 6, 2024

Prioritizing control implementation for dengue prevention and efficiency cost benefits is crucial to the government, decision-makers, policymakers, particularly in resource-limited communities where disease endemic. This study primarily concerned with developing analyzing an optimal model dynamics, which includes asymptomatic, isolation, vigilant compartments human population three time-varying functions. These functions represent personal protection using insecticide-treated bed nets wearing long-sleeved clothes, treatment, vector insecticide spraying. Qualitative analysis of carried out minimize spread costs theory. By classifying all possible combinations interventions into distinct scenarios, single intervention, double triple interventions, effect implementing each intervention scenario illustrated through numerical simulations optimality system. The most efficient identified by computing index intervention. In contrast, scenario's cost-effective strategy obtained infection averted ratio, average cost-effectiveness incremental ratio approaches. Efficiency reveals that combination overall strategy, thereby recommended protect transmission when resource allocations are readily available. communities, treatment regarded can be implemented guide against according analysis.

Language: Английский

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Mathematical analysis of a novel fractional order vaccination model for Tuberculosis incorporating susceptible class with underlying ailment

International Journal of Modelling and Simulation, Journal Year: 2024, Volume and Issue: unknown, P. 1 - 25

Published: July 10, 2024

Language: Английский

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Mathematical modelling of COVID-19 transmission with optimal control and cost-effectiveness analysis

Computer Methods and Programs in Biomedicine Update, Journal Year: 2024, Volume and Issue: 5, P. 100155 - 100155

Published: Jan. 1, 2024

The present global health threat is the novel coronavirus disease (COVID-19), caused by a new strain of SARS-CoV-2 coronavirus. In this study, have employed optimal control theory, aided Pontryagin's Maximum Principle, to explore measures. Specifically, we investigated time-dependent intervention strategies, including proper use personal protective measures and vaccination. Bifurcation analysis was conducted results shows that model system exhibit forward bifurcation. been numerically simulated using fourth-order Runge–Kutta methods. show implementation combination two interventions more significant effective in minimizing spread COVID-19 than single measure. These findings underscore significance multifaceted approaches over singular Notably, combined emerges as markedly containing transmission. Moreover, our study identifies particularly cost-effective intervention, offering substantial relief from burden pandemic within population. We anticipate research will inform evidence-based aid ongoing efforts safeguard public health.

Language: Английский

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Insight into the treatment strategy on pneumonia transmission with asymptotic carrier stage using fractional order modeling approach

Computer Methods and Programs in Biomedicine Update, Journal Year: 2024, Volume and Issue: 5, P. 100134 - 100134

Published: Jan. 1, 2024

Pneumonia remains a significant global health concern, claiming millions of lives annually. This study introduces novel approach by developing and analyzing Caputo fractional order pneumonia infection model that incorporates asymptomatic carriers. Through qualitative lens, we establish the existence uniqueness solutions applying well-known Picard–Lindelöf criteria. Employing next-generation approach, compute model's basic reproduction number, determine equilibrium points, probe their stabilities. The main objective this is to investigate transmission dynamics with focus on carriers using modeling. Our findings reveal innovative outcomes as showcase numerical simulations, providing practical verification results. Notably, explore in-depth, examining influence specific parameters orders disease transmission. contributions lie in advancing theoretical foundation infectious modeling, particularly context pneumonia. rigorous analysis provide valuable insights into behavior proposed model. These hold implications for understanding managing real-world scenarios. serves vital resource researchers, policymakers, healthcare practitioners involved combating preventing spread pneumonia, ultimately contributing efforts public health.

Language: Английский

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A mathematical analysis of the two-strain tuberculosis model dynamics with exogenous re-infection

Healthcare Analytics, Journal Year: 2023, Volume and Issue: 4, P. 100266 - 100266

Published: Sept. 30, 2023

The rise of drug resistance has become a major obstacle in treating tuberculosis (TB), significantly contributing to the increasing disease burden. Therefore, it is essential study transmission dynamics disease, considering factors that contribute strain's impact on burden, using an epidemiological model. We present deterministic mathematical model explores TB with two strains: drug-susceptible and drug-resistant, taking into account exogenous re-infection. thoroughly analyze gain insights behavior qualitative analysis reveals interesting phenomenon known as "backward bifurcation," where both stable disease-free endemic equilibria coexist when associated reproduction number less than one. In absence re-infection, shows existence unique positive equilibria. Numerical simulations were conducted, yielding noteworthy results. Increasing treatment rate for individuals infected strain reduces new cases while detection drug-resistant cases. demonstrate strains can their numbers exceed one without competitive exclusion occurring. summary, this sheds light challenges posed by highlights importance understanding through modeling develop effective strategies its contro.

Language: Английский

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A next-generation matrix approach using Routh–Hurwitz criterion and quadratic Lyapunov function for modeling animal rabies with infective immigrants

Healthcare Analytics, Journal Year: 2023, Volume and Issue: 4, P. 100260 - 100260

Published: Sept. 20, 2023

Rabies remains a major public health concern in many regions of the world, particularly poorer nations. This study proposes mathematical model for animal rabies transmission dynamics, considering infective immigrants and vaccination as potential control measures to address this issue. The effective reproduction number (Re) was calculated by using next-generation matrix approach. By Routh–Hurwitz Criterion, disease-free equilibrium point (DFE) obtained proved be locally asymptotically stable if Re<1 unstable otherwise, also, quadratic Lyapunov function DFE determined globally stable. Moreover, sensitivity analysis parameters on performed normalized forward index method. For simulation analysis, numerical with help MATLAB software. simulated data results revealed that increase rate decreasing will reduce spread decrease, which depicted graphically.

Language: Английский

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A fractional-order nonlinear model for a within-host chikungunya virus dynamics with adaptive immunity using Caputo derivative operator

Healthcare Analytics, Journal Year: 2023, Volume and Issue: 4, P. 100205 - 100205

Published: June 6, 2023

The study of within-host dynamics viral infection is a vital process understanding how healthy cells in the body are affected by foreign bodies and immunity responds to such changes. This paper presents analyses Chikungunya virus transmission with adaptive immune responses using fractional-order derivative operator Caputo type. formulated model describes interaction uninfected cells, infected particles presence Cytotoxic T-Lymphocytes antibody responses. Several analytical methods employed analyse model. Positivity boundedness theory used investigate properties solutions via generalized mean value theorem approach. existence uniqueness examined Banach fixed point method. normalized forward sensitivity method determines different parameters affect system. It was shown that rate representing played significant role model's dynamics. Further, time-dependent optimal control analysed optimize performance approach made popular Pontryagin's maximum principle. Simulations performed visualize theoretical results show influence memory on trajectories concentrations particles, antibodies.

Language: Английский

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A fractional order Monkeypox model with protected travelers using the fixed point theorem and Newton polynomial interpolation

Healthcare Analytics, Journal Year: 2023, Volume and Issue: 3, P. 100191 - 100191

Published: May 9, 2023

This study formulates a Monkeypox model with protected travelers. The fixed point theorem is used to obtain the existence and uniqueness of solution Ulam-Hyers stability for analysis model. Newton polynomial interpolation scheme employed solve an approximate fractional numerical simulations graphical representations suggest that order affects dynamics Monkeypox. shows other underlining transmission trends disease. We conclude result obtained each compartment conforms reality as approaches unity.

Language: Английский

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