Applied Mathematics, Modeling and Simulation, Computational Mathematics, Mathematics
53
Scopus Publications
729
Scholar Citations
20
Scholar h-index
20
Scholar i10-index
Scopus Publications
Analyzing pneumonia transmission with a fractional SVEIR model: the role of vaccination in disease eradication Taruna Garg, Madhuchanda Rakshit, Shyamsunder Discover Public Health, 2026 In recent years, pneumonia has emerged as a significant global health concern, particularly affecting children under five and adults over 65. This study employs the Caputo-Fabrizio fractional derivative to analyze the dynamics of pneumonia using a deterministic Susceptible-Vaccinated-Exposed-Infected-Recovered (SVEIR) model. The research focuses on stability analysis, the basic reproduction number, and equilibrium points within the framework of dynamical systems theory. The study examines disease-free equilibrium states and establishes conditions for their local asymptotic stability. The Lagrange interpolation method is applied to obtain numerical solutions, and MATLAB simulations are conducted to assess the impact of various parameters on disease progression. The reproduction numbers, both with and without vaccination, provide crucial insights into population responses to immunization. A comparative analysis demonstrates that if the vaccination rate surpasses a critical threshold, the prevalence of pneumonia declines, ultimately leading to disease eradication. This study underscores the vital role of vaccination in pneumonia control and presents a mathematical framework for predicting disease behavior under different epidemiological conditions.
Fractional-order modeling of pneumonia transmission with vaccination, reinfection, and data fitting to England cases Agbata Benedict Celestine, Raimonda Dervishi, A. K. Awasthi, Abdul Hamid Ganie, Henri Buçka, Homan Emadifar, Aseel Smerat, Shyamsunder Discover Public Health, 2026 Pneumonia remains a major global health concern, particularly in low- and middle-income countries, where it contributes substantially to morbidity and mortality. In this study, a fractional-order mathematical model was developed to investigate the transmission dynamics of pneumonia, incorporating key control measures such as vaccination, treatment of infected individuals, reinfection dynamics, and environmental interventions. The model employed three types of non-integer order differential operators—Caputo, Caputo–Fabrizio, and Atangana–Baleanu. The existence and uniqueness of solutions were established using fixed-point theory. Model calibration was performed using monthly pneumonia hospitalization data for children aged 0–14 years in England from January 2021 to March 2024, representing a post-COVID phase characterized by increased respiratory illness activity. Parameters were estimated through least-squares optimization under biologically realistic constraints, and the simulated results showed strong agreement with observed hospitalization trends, confirming the model’s validity. Numerical simulations demonstrated that higher fractional orders reduce transmission speed, lower the peak number of cases, and extend outbreak duration, reflecting the memory-dependent nature of fractional systems. Sensitivity analysis further revealed that effective environmental interventions and prompt treatment of infected individuals play a crucial role in reducing disease transmission. The study provided a robust and flexible approach to understanding pneumonia dynamics and highlights the importance of integrating vaccination, timely treatment, and environmental improvements as complementary strategies to sustainably reduce the pneumonia burden.
On the existence of solutions to psi-Hilfer fractional neutral integro-differential equations with delay Vinitha Ravi, Nirmalkumar Rajendran, Shyamsunder Studia Universitatis Babes Bolyai Mathematica, 2026 This paper investigates a class of neutral-type fractional differential equations with finite delays, formulated through the generalized psi-Hilfer fractional derivative. This operator, being a broad framework that unifies various fractional derivatives, is highly effective in modeling dynamical processes with memory and hereditary characteristics. The primary objective is to establish sufficient conditions for the existence and uniqueness of solutions to such equations. The analysis employs fixed point theory—specifically Banach’s contraction principle and Krasnoselskii’s fixed point theorem—within an appropriately weighted function space. These tools ensure that the solutions are not only well-defined but also uniquely determined. Furthermore, two stability notions, namely Ulam–Hyers stability and its generalized form, are studied to verify that solutions remain close to the expected behavior under small perturbations in initial conditions or parameters. To demonstrate the applicability of the theoretical framework, an illustrative example with explicit functions and parameters is provided. The results strengthen the theoretical foundations of fractional calculus and open directions for further research on more generalized and complex delayed fractional systems.
A study of fractional calculus operators associated with the family of W-function Mathematics in Engineering Science and Aerospace, 2026
Memory-Driven Dynamics of Hepatitis B Transmission Incorporating Media Awareness Kaushal Soni, Shyamsunder, Arvind Kumar Sinha Advanced Theory and Simulations, 2026 In this study, we develop a novel fractal‐fractional mathematical model for the transmission dynamics of Hepatitis B virus (HBV) incorporating treatment and media‐driven awareness. The model is formulated using the Atangana–Baleanu–Caputo fractal‐fractional operator, which effectively captures both memory effects and the heterogeneous (fractal) nature of disease transmission. Unlike classical integer‐order models, this approach provides a more realistic description of HBV dynamics by accounting for nonlocal interactions and long‐term dependencies. The proposed model is analyzed qualitatively by establishing key mathematical properties, including positivity, boundedness, existence, and uniqueness of solutions. The basic reproduction number is derived to examine the threshold behavior of the system, and the stability of equilibrium points is investigated. Numerical simulations are carried out to illustrate the impact of key parameters on disease progression. The results show that increasing media awareness significantly reduces the susceptible and infected populations by promoting preventive behavior, while improved treatment rates enhance recovery. Moreover, the fractal‐fractional framework reveals persistent memory effects, indicating that past disease states play an important role in shaping current dynamics. These findings highlight the importance of combining treatment strategies with awareness programs to effectively control HBV transmission and provide useful insights for public health policy design.
Numerical simulation and fractional-order analysis of COVID-19–Zika co-infection: Impacts of vaccination, treatment, and vector control Nonlinear Studies, 2025
Evaluation of improper integrals involving incomplete I-functions and related special forms Mathematics in Engineering Science and Aerospace, 2025
A Mathematical Modelling Approach to the Long-Term Global Impacts of COVID-19 AB Celestine, AQ Ojoma, H Emadifar, M Gumus, Shyamsunder, A Smerat International Journal of Mathematics for Industry , 2026 2026
Investigating Controllability in Hilfer-Katugampola Fractional Equations: Impulsive and Neutral Dynamics with Non-local Effects A Prabha, R Nirmalkumar, Shyamsunder Proyecciones (Antofagasta) 45 (2), 256-266 , 2026 2026
Generalized Composite Fractional Derivatives and Integral Operators With Incomplete R-Function Kernels P Purohit, R Gupta, Shyamsunder, B Shimelis International Journal of Mathematics and Mathematical Sciences 2026 (1), 2307705 , 2026 2026
Fractal-fractional dynamics of HIV/AIDS: unveiling the synergistic impact of condoms, prophylaxis, and antiretroviral interventions for epidemic control GO Acheneje, J Amos, E Abah, W Atokolo, AB Celestine, Shyamsunder, ... Iranian Journal of Numerical Analysis and Optimization 16 (2), 385–446 , 2026 2026
Memory-Driven Dynamics of Hepatitis B Transmission Incorporating Media Awareness K Soni, Shyamsunder, AK Sinha Advanced Theory and Simulation 9 (5), e70394 , 2026 2026
Impact of Vaccination on COVID-19 using Fractional Operators with Non-local Kernel R Sharma, SS Sharma, Shyamsunder, P Upreti Journal of Prime Research in Mathematics, 135-160 , 2026 2026
Determination of Blood Glucose Levels Using the Incomplete H-Function M Meena, VK Meena, MM Gour, Shyamsunder Journal of Applied Nonlinear Dynamics 15 (2), 303-311 , 2026 2026
Impact of fractional order on reaction rates: Solutions to kinetic equations with incomplete ℵ-function Shyamsunder, D Gangwar Computational Methods for Differential Equations 14 (2), 581-589 , 2026 2026 Citations: 1
Drug Delivery to the Bloodstream within the Cardiovascular System using Caputo-Fabrizio Fractional Derivatives M Yaceena, PSS Uduman, Shyamsunder, VS Panwar Chaos Theory and Applications 8 (1), 1-8 , 2026 2026
A FRACTIONAL-ORDER MODEL FOR DRUG DISTRIBUTION VIA GASTROINTESTINAL AND INTRAVENOUS ROUTES USING THE CAPUTO-FABRIZIO OPERATOR SM Yaceena, PSS Uduman, S Kumawat, D Fathima JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES 21 (3), 153-175 , 2026 2026
Fractional-order modeling of pneumonia transmission with vaccination, reinfection, and data fitting to England cases BC Agbata, R Dervishi, AK Awasthi, AH Ganie, H Buçka, H Emadifar, ... Discover Public Health 23 (290), 1-38 , 2026 2026 Citations: 1
Optimal Control and Bifurcation Analysis of Cholera Model TL Tirfe, LL Obsu, ED Gurmu, AB Celestine, Shyamsunder Journal of Prime Research in Mathematics, 1-28 , 2026 2026
Unified Analysis of Comprehensive Finite Integrals Using Srivastava Polynomial and ℵ-Function Shyamsunder, M Meena Palestine Journal of Mathematics 15 (Special Issue I), 143-153 , 2026 2026
Certain Expansion Formulae of Incomplete Yang Y -Function MC Khatumariya, V Agarwal, Shyamsunder Palestine Journal of Mathematics 15 (Special Issue I), 245-254 , 2026 2026
Certain Generating Function Involving The Incomplete Yang Y-Function VK Raiger, V Agarwal, Shyamsunder Palestine Journal of Mathematics 15 (Special Issue I), 255-263 , 2026 2026
Novel Findings on the Srivastava-Luo-Raina M-Transform with Applications to Incomplete W-Functions R Sharma, SS Sharma, Shyamsunder Palestine Journal of Mathematics 15 (Special Issue I), 96-109 , 2026 2026
Numerical solution of fractional order typhoid fever model via the generalized fractional Adams-Bashforth-Moulton approach E Jalija, J Amos, W Atokolo, E Abah, BC Agbata, GO Acheneje, ... Network Modeling Analysis in Health Informatics and Bioinformatics 15 (68), 1-26 , 2026 2026
Analyzing pneumonia transmission with a fractional SVEIR model: the role of vaccination in disease eradication T Garg, M Rakshit, Shyamsunder Discover Public Health 23 (36) , 2026 2026
A Study of Fractional Kinetic Equations Incorporating Incomplete R‐Function Kernels P Purohit, R Gupta, Shyamsunder, DL Suthar Journal of Mathematics 2026 (1) , 2026 2026
A Mathematical Analysis of Non-linear Smoking Model via Fractional Operators S Panwar, RM Pandey, SD Purohit, Shyamsunder Computational Methods for Differential Equations 14 (01), 60-80 , 2026 2026
MOST CITED SCHOLAR PUBLICATIONS
A new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks Shyamsunder, S Bhatter, K Jangid, A Abidemi, KM Owolabi, SD Purohit Decision Analytics Journal 6, 100156 , 2022 2022 Citations: 94
A novel study of the impact of vaccination on pneumonia via fractional approach Shyamsunder, SD Purohit Partial Differential Equations in Applied Mathematics 10 (2024), 100698 , 2024 2024 Citations: 47
Numerical modeling on age-based study of coronavirus transmission S Kumawat, S Bhatter, DL Suthar, SD Purohit, K Jangid Applied Mathematics in Science and Engineering 30 (1), 609-634 , 2022 2022 Citations: 40
Fractionalized mathematical models for drug diffusion Shyamsunder, S Bhatter, K Jangid, SD Purohit Chaos, Solitons & Fractals 165, 112810 , 2022 2022 Citations: 38
A Mathematical Model of the Dynamics of the Transmission of Monkeypox Disease Using Fractional Differential Equations M Manivel, A Venkatesh, K Arunkumar, M Prakash Raj, Shyamsunder Advanced Theory and Simulations, 2400330 , 2024 2024 Citations: 36
A novel investigation of the hepatitis B virus using a fractional operator with a non-local kernel M Meena, M Purohit, Shyamsunder, SD Purohit, KS Nisar Partial Differential Equations in Applied Mathematics 8, 100577 , 2023 2023 Citations: 36
A fractional mathematical model for vaccinated humans with the impairment of Monkeypox transmission A Venkatesh, M Manivel, K Arunkumar, M Prakash Raj, Shyamsunder, ... The European Physical Journal Special Topics, 1-21 , 2024 2024 Citations: 34
Numerical study of a new time-fractional Mpox model using Caputo fractional derivatives A Venkatesh, M Manivel, B Baranidharan, Shyamsunder Physica Scripta 99 (2), 025226 , 2024 2024 Citations: 34
A novel fractionalized investigation of tuberculosis disease M Meena, M Purohit, Shyamsunder, SD Purohit, D Baleanu, DL Suthar Applied Mathematics in Science and Engineering 32 (2024), 2351229 , 2024 2024 Citations: 31
A comprehensive study of monkeypox disease through fractional mathematical modeling M Manivel, A Venkatesh, S Kumawat Math. Model. Numer. Simul. Appl 5 (1), 65-96 , 2025 2025 Citations: 29
A STUDY OF THE HEPATITIS B VIRUS INFECTION USING HILFER FRACTIONAL DERIVATIVE SHYAMSUNDER, S BHATTER, K JANGID, SD PUROHIT Proceedings of the Institute of Mathematics and Mechanics 48, 100-117 , 2022 2022 Citations: 28
A new investigation on fractionalized modeling of human liver S Bhatter, K Jangid, S Kumawat, D Baleanu, SD Purohit, DL Suthar Scientific Reports 14 (1), 1636 , 2024 2024 Citations: 27
Numerical simulation for the co-infection of Monkeypox and HIV model using fractal-fractional operator M Manivel, A Venkatesh, S Kumawat Modeling Earth Systems and Environment 11 (3), 157 , 2025 2025 Citations: 26
A novel investigation of the influence of vaccination on pneumonia disease Shyamsunder, SD Purohit, DL Suthar International Journal of Biomathematics, 2450080 , 2024 2024 Citations: 26
Mathematical analysis using fractional operator to study the dynamics of dengue fever M Meena, M Purohit, Shyamsunder Physica Scripta 99 (2024), 095206 , 2024 2024 Citations: 24
A study of incomplete I -functions relating to certain fractional integral operators S Bhatter, Nishant, Shyamsunder, SD Purohit, DL Suthar Applied Mathematics in Science and Engineering 31 (1), 2252996 , 2023 2023 Citations: 24
Fractional differential equations related to an integral operator involving the incomplete I ‐function as a kernel S Bhatter, S Kumawat, K Jangid, SD Purohit, HM Baskonus Mathematical Methods in the Applied Sciences 46 (14), 15033-15047 , 2023 2023 Citations: 24
A generalized study of the distribution of buffer over calcium on a fractional dimension S Bhatter, K Jangid, S Kumawat, SD Purohit, D Baleanu, DL Suthar Applied Mathematics in Science and Engineering 31 (1), 2217323 , 2023 2023 Citations: 21
Determining glucose supply in blood using the incomplete I-function S Bhatter, K Jangid, Shyamsunder, SD Purohit Partial Differential Equations in Applied Mathematics, 100729 , 2024 2024 Citations: 20
Analysis of the family of integral equation involving incomplete types of I and Ī -functions S Bhatter, K Jangid, S Kumawat, D Baleanu, DL Suthar, SD Purohit Applied Mathematics in Science and Engineering 31 (1), 2165280 , 2023 2023 Citations: 20