A Fractional-Order Pneumonia Transmission Model Using the Generalised Atangana–Baleanu Derivative: Analysis and Numerical Simulations | Chapter 3 | New Horizons of Science, Technology and Culture Vol. 8

 

Pneumonia remains a major global health burden, especially among children under five and the elderly, and is a leading cause of death in many low- and middle-income countries. In this paper, we formulate a novel fractional pneumonia model utilising the generalized Atangana–Baleanu (GAB) derivative. Pneumonia remains a global health threat, particularly in regions with limited medical infrastructure. We extend the traditional integer-order compartmental model into a fractional framework to capture the hereditary properties and memory effects of disease transmission. We establish the existence and uniqueness of solutions for all compartments (Vaccinated V, Susceptible S, Carrier C, Infected I, and Recovered R) using fixed-point theory. This mathematical foundation ensures the biological feasibility of our memory-dependent model, which has significant implications for understanding persistent transmission patterns in pneumonia epidemiology. A numerical scheme based on Newton polynomial interpolation is derived. Finally, we discuss the comparative dynamics of the model relative to data trends for Iowa and Mississippi, demonstrating that fractional-order derivatives provide superior flexibility in fitting localised epidemic spikes compared to traditional models. Our key finding shows that regions with higher vaccination efficacy experience significantly flattened epidemic curves, highlighting the critical importance of vaccination coverage in pneumonia control strategies.

 

 

Author(s) Details

Khan Sana Rahman
Department of Applied Science, Everest College of Engineering and Technology, Chhatrapati Sambhajinagar, Maharashtra, India.

 

Please see the book here :- https://doi.org/10.9734/bpi/nhstc/v8/7117

The Uniqueness of Random Solution to Itô Stochastic Integral Equation | Chapter 2 | Mathematics and Computer Science: Contemporary Developments Vol. 7

The integral equation of Itô integral type is considered, for the deterministic and stochastic cases. We show that under some assumptions the equations have solutions belonging to the space of continuous functions. In this study, we attempt to apply the theoretical techniques of probabilistic functional analysis to examine of existence and Uniqueness of a Random Solution to Itô Stochastic Integral Equation. Also, we shall present another type of stochastic integral equation that has been of considerable importance to applied mathematicians and engineers, involving the Itô or Itô-Doob form of stochastic integrals. We present the extension when W = (W¹, ... ,W^d) is a multidimensional Brownian motion and we replaced the minimal augmented filtration generated by \(W, \mathbb{F}^w\)={\({\mathcal{F}^w_t}\)}\(_{t\epsilon\lceil0,T\rceil}\) by a largest one \(\mathbb{H}=\){\({\mathcal{H}^w_t}\)}\(_{t\epsilon\lceil0,T\rceil}\) (satisfying the usual conditions)  such that the Brownian motion W is a martingale respect to \(\mathbb{H}\) ; i.e., the following property is satisfied \(\mathbb{E}\left[W_t - W_s : \mathcal{H}_s\right]\) = 0 and We have constructed the Itô integral for processes in \(h \epsilon L^0_{\alpha,_T}\) by localizing \(h\) in \(L^2_{\alpha,_T}\). i.e. by considering \(h^n\) = \(h1\)\(_{[{0,T_n}]}\).       

 

Author (s) Details

 

Hamdin Ahmed Alafif
Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v7/1821

Fixed Points Theorem of a Countable Family of I-Nonexpansive Multivalued Mappings of Modified Iteration in Banach Spaces | Chapter 2 | Current Topics on Mathematics and Computer Science Vol. 11

In this chapter, I provide a modified Ishikawa iteration for a countable family of multi-valued Mappings under the SC- and Condition constraints (A). The optimum approximation operator for the modified Ishikawa iteration in Banach spaces to attain weak and strong convergence. The challenge of identifying a common fixed point for a countable family of I-Nonexpansive multi-valued mappings yielded the following main results.

Author (S) Details

Poonam Lata Prabhakar

Samrat Ashok Technological Institute, Vidisha, India.

View Book :- stm.bookpi.org/CTMCS-V11/article/view/3976