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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Novel intelligent predictive networks for analysis of chaos in stochastic differential SIS epidemic model with vaccination impact

Mathematics and Computers in Simulation, Journal Year: 2023, Volume and Issue: 219, P. 251 - 283

Published: Dec. 19, 2023

Language: Английский

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Robustness and exploration between the interplay of the nonlinear co-dynamics HIV/AIDS and pneumonia model via fractional differential operators and a probabilistic approach

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

Published: July 23, 2024

Abstract In this article, we considered a nonlinear compartmental mathematical model that assesses the effect of treatment on dynamics HIV/AIDS and pneumonia (H/A-P) co-infection in human population at different infection stages. Understanding complexities co-dynamics is now critically necessary as consequence. The aim research to construct H/A-P context fractional calculus operators, white noise probability density functions, employing rigorous biological investigation. By exhibiting system possesses non-negative bounded global outcomes, it shown approach both mathematically biologically practicable. required conditions are derived, guaranteeing eradication infection. Furthermore, adequate prerequisites established, configuration tested for existence an ergodic stationary distribution. For discovering system’s long-term behavior, deterministic-probabilistic technique modeling designed operated MATLAB. extensive review, hope previously mentioned improves leads mitigating two diseases their co-infections by examining variety behavioral trends, such transitions unpredictable procedures. addition, piecewise differential strategies being outlined having promising potential scholars range contexts because they empower them include particular characteristics across multiple time frame phases. Such formulas can be strengthened via classical techniques, power law, exponential decay, generalized Mittag-Leffler kernels, functions random get accurate description function encircling quasi-equilibrium point if minimizes propagation co-dynamics. Consequently, obtain better outcomes when analyzing facts using perturbations implementing these challenging issues. Random crucial controlling spread epidemic whenever suggested circulation steady amount eliminated closely correlated with perturbation level.

Language: Английский

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A non-linear deterministic mathematical model for investigating the population dynamics of COVID-19 in the presence of vaccination

Healthcare Analytics, Journal Year: 2024, Volume and Issue: 5, P. 100328 - 100328

Published: April 8, 2024

COVID-19 has been a significant threat to many countries worldwide. remains even in the presence of vaccination. The study formulates and analyzes non-linear deterministic mathematical model investigate dynamics Numerical results show that increasing treatment rates with relatively high vaccination rate might subdue virus population. Also, decreasing vaccine inefficacy increases efficacy, this may result population free virus. We further as against inefficacy, effective contact for modification parameter accounts increased infectiousness COVID-19, responsible can be eradicated from sensitivity analysis deduce hidden factors are driving dynamics. These must given special attention minimized. includes incubation periods vaccinated unvaccinated individuals, fractions transition individuals

Language: Английский

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Stochastic Runge–Kutta for numerical treatment of dengue epidemic model with Brownian uncertainty

Modern Physics Letters B, Journal Year: 2024, Volume and Issue: unknown

Published: May 30, 2024

The current challenge faced by the global research community is how to effectively address, manage, and control spread of infectious diseases. This focuses on conducting a dynamic system analysis stochastic epidemic model capable predicting persistence or extinction dengue disease. Numerical methodology deterministic procedures, i.e. Adams method stochastic/probabilistic schemes, Runge–Kutta method, employed simulate forecast study specifically employs two nonlinear mathematical systems, namely vector-borne (DVBDE) (SVBDE) models, for numerical treatment. objective dynamics these models ascertain their behavior. VBDE segmented population into following five classes: susceptible population, infected recovered mosquitoes, mosquitoes. approximate solution evolution each calculated generating significant number scenarios varying population’s recovery rate, human birth mosquitoes contaminated people coming contact with healthy people, mortality rate mosquitos death mosquito that not infected. Comparative evaluations are presented, highlighting unique characteristics performance, through execution simulations results.

Language: Английский

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Modeling and numerical analysis of a fractional order model for dual variants of SARS-CoV-2

Alexandria Engineering Journal, Journal Year: 2022, Volume and Issue: 65, P. 427 - 442

Published: Oct. 20, 2022

This paper considers the novel fractional-order operator developed by Atangana-Baleanu for transmission dynamics of SARS-CoV-2 epidemic. Assuming importance non-local approach, mechanism has been investigated while taking into account different phases infection and various routes disease. To conduct proposed study, first all, we shall formulate model using classical ordinary derivatives. We utilize fractional order derivative will be extended to a containing The being used is differential Φ1. analyzed further some basic aspects are besides calculating reproduction number possible equilibria model. examined stability purposes necessary conditions obtained. Stability also in terms numerical setup. theory non-linear functional analysis employed Ulam-Hyers's presented. approach newton's polynomial considered new scheme which helped presenting an iterative process ABC system. Based on this scheme, sample curves obtained values Φ1 pattern derived between derivative. Further simulations presented show cruciality parameters impact such control disease findings study provide strong conceptual insights mechanisms contagious diseases, assisting global professionals developing policies.

Language: Английский

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Bifurcation analysis of a discrete-time prey-predator model

Bulletin of Biomathematics, Journal Year: 2023, Volume and Issue: unknown

Published: Oct. 9, 2023

This paper investigates the importance of studying dynamics predator-prey systems and specific significance Neimark-Sacker period-doubling bifurcations in discrete-time prey-predator models. By conducting a numerical bifurcation analysis examining diagrams phase portraits, we present important results that differentiate our study from others field. Firstly, reveals occurrence model under certain parameter values. These lead to emergence stable limit cycles characterized by complex unpredictable dynamics. finding emphasizes inherent complexity nonlinearity contributes deeper understanding their Additionally, highlights advantages limitations employing models population research. The use allows for more tractable while still capturing significant aspects ecological systems. In conclusion, this holds shedding light on role bifurcations. Our findings contribute offer implications management strategies.

Language: Английский

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Fractional and stochastic modeling of breast cancer progression with real data validation

PLoS ONE, Journal Year: 2025, Volume and Issue: 20(1), P. e0313676 - e0313676

Published: Jan. 10, 2025

This study presents a novel approach to modeling breast cancer dynamics, one of the most significant health threats women worldwide. Utilizing piecewise mathematical framework, we incorporate both deterministic and stochastic elements progression. The model is divided into three distinct phases: (1) initial growth, characterized by constant-order Caputo proportional operator (CPC), (2) intermediate modeled variable-order CPC, (3) advanced stages, capturing fluctuations in cell populations using operator. Theoretical analysis, employing fixed-point theory for fractional-order phases Ito calculus phase, establishes existence uniqueness solutions. A robust numerical scheme, combining nonstandard finite difference method fractional models Euler-Maruyama system, enables simulations progression under various scenarios. Critically, validated against real data from Saudi Arabia spanning 2004-2016. Numerical accurately capture observed trends, demonstrating model’s predictive capabilities. Further, investigate impact chemotherapy its associated cardiotoxicity, illustrating different treatment response scenarios through graphical representations. fractional-stochastic offers powerful tool understanding predicting potentially informing more effective strategies.

Language: Английский

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Stochastic perspective to a SIVA in-host model of DENV transmission

Journal of Nonlinear Complex and Data Science, Journal Year: 2025, Volume and Issue: unknown

Published: April 17, 2025

Abstract The viral transmission is a complex process which influenced by certain factors such as infection rate, production rate of new viruses and impact the antibody-virus complex. These affect unpredictably under influence external noise. In order to incorporate this phenomenon, manifested random environment introducing noise deterministic SIVA model formulated dividing dynamical system into four distinct parts, namely, susceptible cells ( S ), infected I virus V ) immune A ). analyzed representation real-life situations that involves assumptions. derive intensity fluctuations variances cell population stochastic with presence Gaussian white noise, Fourier transformation method used. exhibits two equilibria: virus-free steady (VFS) endemic (ES) state. intensities different populations are derived values computed numerically. results sensitivity analysis, shown in graphical form, indicate highly sensitive. Our findings suggest causes model, leading noticeable on virus.

Language: Английский

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Co-Dynamics of COVID-19 and Viral Hepatitis B Using a Mathematical Model of Non-Integer Order: Impact of Vaccination

Fractal and Fractional, Journal Year: 2023, Volume and Issue: 7(7), P. 544 - 544

Published: July 14, 2023

The modeling of biological processes has increasingly been based on fractional calculus. In this paper, a novel fractional-order model is used to investigate the epidemiological impact vaccination measures co-dynamics viral hepatitis B and COVID-19. To existence stability new model, we use some fixed point theory results. COVID-19 thresholds are estimated using fitting. vaccine parameters plotted against transmission coefficients. effect non-integer derivatives solution paths for each state trajectory diagram infected classes also examined numerically. An infection-free steady an infection-present equilibrium achieved when R0<1 R0>1, respectively. Similarly, phase portraits confirm behaviour components, showing that, regardless order derivative, trajectories disease always converge toward states over time, no matter what initial conditions assumed diseases. verified real observations.

Language: Английский

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