Celebrating GHAIR’s contributions to independent research, academic excellence, and global collaboration.
Awards & Recognitions
Honouring Excellence and Research Achievement
GHAIR has been recognised for its contributions to independent research, academic innovation, and scholarly collaboration. These awards represent our ongoing efforts to advance knowledge and support impactful research outcomes.
The Ebola virus is a highly infectious disease that can propagate throughout a population depending on how people interact in society. his research introduces a modified mathematical model of Ebola Virus Disease (EVD), incorporating effective control strategies such as quarantine, self-isolation, and hospitalization. These compartments have played a key role in understanding the transmission of the Ebola virus disease in the society. By using a conformable derivative, a system of equations has been developed for the Ebola virus disease model. The basic reproduction number R_0 has been determined using the Next-generation matrix method. To understand the impact of parameter variations on Ebola virus disease, sensitivity analysis of R_0 has been observed. Stability analysis has been calculated at both the {DFEP} and the DPEP to assess the behaviour of virus. {The conformable derivative facilitates a smooth transition from fractional order to classical models as the parameter (c) approaches to 1. Additionally, implementation of quarantine, self-isolation, and hospitalization emerges as a highly effective strategy, significantly reduced Ebola virus disease in society}. These findings enhance our understanding of Ebola dynamics and offer critical implications for effective outbreak control strategies.
Malaria remains one of the most serious and widespread vector-borne infectious diseases globally, caused by Plasmodium protozoa and transmitted through bites of infected female Anopheles mosquitoes. In this study, we develop a novel integrative bioinformatics-driven deterministic mathematical model to capture the complex transmission dynamics of malaria. Our model distinguishes between homogeneous and heterogeneous exposed human compartments (Ehm, Eht) and explicitly incorporates mosquito population dynamics. The coupled system comprises human compartments SM, Ehm, Eht, IM, HM, RM and mosquito compartments SF , EF , IF . We conduct a thorough stability analysis of the malaria-free equilibrium, evaluating both local and global stability in relation to the basic reproduction number R0. Sensitivity analysis identifies the biting rate αM and infection probability βM as critical parameters driving disease transmission. To assess intervention efficacy, we integrate time-dependent control strategies and formulate an optimal control problem using Pontryagin’s Maximum Principle. The control variablesinclude bed net usage (m1), medication treatment (m2), and insecticide spraying (m3). Numerical simulations, implemented via a fourth-order Runge-Kutta scheme, demonstrate the effectiveness of these interventions in reducing both exposed and infected populations. Our findings underscore the importance of targeted, time-optimized control measures and validate the utility of combining bioinformatics with mathematical modeling to inform malaria control policies.
A novel non-linear fractional alcohol consumption model using the Atangana–Baleanu Caputo (ABC) fractional derivative has been developed in this study. Using sophisticated mathematical methods and the finite difference method, the model is developed to reflect the intricate dynamics of alcohol consumption. Several fundamental theorems connected to the ABC fractional derivative have been thoroughly demonstrated, ensuring the validity and dependability of the model when examining complex systems. Numerical simulations validate the theoretical findings, confirming the model’s high accuracy and convergence. The findings emphasize that increasing the rate of people taking treatment cause decreasing the interaction rates between heavy and non-heavy alcohol drinkers. This framework provides useful information to develop successful strategies for intervention for alcohol dynamics.
This study aims to develop a mathematical model to identify key factors influencing the anti-tumor response. We have been proposed a nonlinear fractional-order tumor dynamics model (LPIHE) using a novel piecewise approach. This model incorporates the effects of estrogen, providing a comprehensive understanding of tumor behavior and offering insights into using estrogen to control tumor growth. To validate the model, we establish the existence and uniqueness of solutions for the piecewise derivative system under Arzelà-Ascoli and Schauder conditions. To assess biological feasibility, we have been calculated the reproductive number
and conduct a sensitivity analysis. Key parameters are systematically varied to analyze their impact, providing insights into the model’s robustness and vulnerability. Newton’s polynomial approach is used to obtain numerical solutions with real data across various fractional orders. This model have been investigated the effects of classical and modified fractional calculus operators, with a particular focus on the classical Caputo piecewise operator. Results indicate that higher estrogen levels reduce tumor growth rates, underscoring the importance of fractional operators in modeling tumor dynamics.
This paper focuses on modeling and analyzing a nonlinear fractional Maxwell fluid across a vertical plate using a novel definition of the Caputo fractional derivative. Specifically, the newly formulated fractional definition is tailored for the finite difference method. Buoyancy effects are considered to bring the model closer to the natural occurrences of the magnetic field. The novel fractional derivative definition of the designed model has been implemented, and the results have been further analyzed using theoretical and numerical methods. Significant theorems are also included in the study. A simulation was performed to determine which fractional derivative operator is more accurate than the others. The designed definition demonstrates a high convergence rate and decreased computational cost, both of which are primary objectives. Graphs have also been plotted to illustrate the velocity and temperature distributions as the physical parameters vary.
Norovirus is a highly contagious pathogen responsible for numerous outbreaks of gastrointestinal disease and poses a significant public health challenge. In this study, we propose a modified Caputo–Fabrizio fractal–fractional model of norovirus. This model consists of seven compartments (NoV7), including susceptible S (t) , exposed E (t) , infected U (t) , quarantined Q (t) , clinically-positive P (t) , vaccinated V (t) , and recovered R (t) individuals and has been developed to explain the transmission dynamics of norovirus. We have determined the basic reproduction number, R 0 , which estimates the virus’s ability to spread. Both local and global stabilities have been investigated at the infection-free equilibrium point. Furthermore, sensitivity analysis is conducted to evaluate the influence of each parameter on R 0 , providing insights into how changes in these parameters (ϖ , , γ) affect the virus’s transmission dynamics. The basic mathematical model has been expanded to include time-dependent control variables, leading to the development of an optimal control model using various control strategies. Analysis utilizing the Pontryagin maximum principle has determined the conditions for optimal pandemic control. Numerical results indicate that applying control strategies to the fractal–fractional mathematical model in the sense Caputo–Fabrizio, specifically vaccination ( a 1 ) and hospitalization ( a 2 ), results in a decreased rate of norovirus transmission. The fractal–fractional model provides a more comprehensive understanding of the dynamical behavior and memory effects. This study aids in understanding the dynamic behavior of the mathematical model and the impact of control strategies, which can minimize the spread of infection.
Corruption can be defined as the misuse of power, of public office, or of authority entrusted to the state for one’s benefit, thus bringing to light the lack of transparency, accountability, and fairness in public and private sectors. In this context, we introduce a fresh compartmental model for corruption dynamics which fully aligns theoretical assumptions to empirical realities. The different individuals are divided into the five compartments, namely, susceptible, corrupt, under investigation, jailed, and honest. To introduce memory and lineage effects in the corruption dynamics, the Atangana–Baleanu–Caputo fractional derivative is utilized. Applying the next-generation matrix method, we determine the basic reproduction number, which acts as a threshold parameter for the survival of corruption in the system. The case corresponds to the situation where the corruption-free equilibrium enjoys both local and global asymptotic stability, while
results in the endemic equilibrium (corruption-present) being asymptotically stable. Additionally, the bifurcation analysis is used to expound the parameter-induced transitions in the level of corruption and to pinpoint the main intervention mechanisms. The model now achieves improved predictive accuracy through the implementation of an artificial neural network (ANN) method. The ANN accurately models the system behavior and encompasses complex nonlinear traits. The ANN-derived predictions match the numerical simulations conducted with Maple 19 and the Lagrange interpolation technique almost perfectly. The results indicate that anti-corruption measures carefully chosen according to the model can lead to a substantial decrease in corruption thus proving the usefulness of the proposed model for political evaluation and strategy-making.
In this research, the ongoing COVID-19 disease by considering the vaccination strategies into mathematical models is discussed. A modified and comprehensive mathematical model that captures the complex relationships between various population compartments, including susceptible (Sα), exposed (Eα), infected (Uα), quarantined (Qα), vaccinated (Vα), and recovered (Rα) individuals. Using conformable derivatives, a system of equations that precisely captures the complex interconnections inside the COVID-19 transmission. The basic reproduction number (R0), which is an essential indicator of disease transmission, is the subject of investigation calculating using the next-generation matrix approach. We also compute the R0 sensitivity indices, which offer important information about the relative influence of various factors on the overall dynamics. Local stability and global stability of R0 have been proved at a disease-free equilibrium point. By designing the finite difference approach of the conformable fractional derivative using the Taylor series. The present methodology provides us highly accurate convergence of the obtained solution. Present research fills research addresses the understanding gap between conceptual frameworks and real-world implementations, demonstrating the vaccination therapy’s significant possibilities in the struggle against the COVID-19 pandemic.
This paper provides a mathematical model of HIV dynamics that involves the interactions between HIV and the human immune system with a certain combination of proteins and fatty acids, especially omega-3. In order to explain CD4 T cell HIV infection, the model is formulated as a system of nonlinear differential equations. Using the next-generation matrix method, we calculate the basic reproduction number (R_0) and analyze the stability of the infection-free equilibrium. The given results indicate that the equilibrium is both locally and globally asymptotically stable when R_01. An important feature in this paper is the use of Artificial Neural Networks (ANNs) to determine the numerical solutions of the system, which increases the accuracy and computation speed of the model solutions. A sensitivity analysis of R_0 is conducted to identify critical parameters that determine the spread of HIV. Numerical simulations are performed using a fourth-order Runge–Kutta (RK4) method to understand the effects of nutritional interventions. The results prove that a specific combination of proteins, omega-3, and omega-6 fatty acids may be a potential way to control the immune response and change the progression of HIV and find a new approach to managing the disease.
In December 2019, the SARS-CoV-2 (COVID-19) virus was identified and quickly spread worldwide, causing a major global health crisis. To investigate its transmission dynamics, we developed a ten-compartment mathematical model, named CoVCom10, which includes key stages such as asymptomatic (F), pre-symptomatic (E), and vaccinated (V ) individuals. The basic reproduction number (R0) has been calculated to evaluate how easily the virus can spread. We analyzed the local and global stability of the disease-free equilibrium and prove that the disease under control after vaccination when R0 < 1. A sensitivity analysis was conducted to assess the impact of key parameters, including the vaccination rate from susceptible individuals (β), trans-
mission from susceptible to pre-symptomatic individuals (φ), and the rate of vaccination from pre-symptomatic individuals (γ). To evaluate intervention strategies, we extended the model by incorporating time-dependent control variables representing vaccination (a1), hospitalization (a2), and isolation of asymptomatic individuals (a3). The Pontryagin Maximum Principle was applied to identify optimal control strategies. Numerical simulations reveal that these interventions significantly reduce virus transmission, particularly as the fractional-order parameter (ς) approaches 1, which aligns with observed real-world disease dynamics. The study emphasizes the effectiveness of integrated vaccination and treatment strategies in controlling the spread of COVID-19.
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Achievements Timeline
Our Journey of Achievement and Growth
2025
Launch of multiple independent research projects
Expansion of international research collaborations
2024
Successful academic seminars & workshops
Increased researcher participation globally
2023
Successful academic seminars & workshops
Increased researcher participation globally
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