Journal of Mathematical Analysis and Modeling

Implementation of Fractional Blood Ethanol Model by Computation of Matrix Mittag–Leffler Functions

Shyamsunder - — 2025-12-31

The article discusses several innovative and intriguing aspects of the fractional operator-based fractional blood ethanol concentration model involving first-order chemical reactions. The most commonly used fractional operator, Caputo, performs the analysis. The analytical results of blood ethanol concentration are examined utilizing the computation matrix Mittag-Leffler function (MMLF). Solutions' ethanol concentrations are displayed as an extended series. A graphical representation of the effect of fractional parameters on ethanol concentrations is provided.

The comparative analysis for concentrations demonstrates the proposed model's novel composite fractional derivative properties.

According to studies, fractional models approximate real data more correctly than their integer order derivative operator counterparts.

The fractional blood alcohol models presented provide essential and beneficial results that can be used to forecast future information for the medical community.

Note for Line and Total SuperHyperGraphs: Connecting Vertices, Edges, Edges of Edges, Edges of Edges of Edges in Hierarchical Systems

Takaaki Fujita — 2025-12-31

Hypergraphs extend classical graphs by allowing hyperedges to connect any nonempty subset of vertices,
thereby capturing complex group-level relationships. Superhypergraphs advance this framework by introducing
recursively nested powerset layers, enabling the representation of hierarchical and self-referential links among
hyperedges. A line graph encodes the adjacencies between edges of an original graph by transforming each
edge into a vertex and connecting two vertices if their corresponding edges share a common endpoint. A total
graph incorporates both the vertices and edges of the original graph as its own vertices, with edges representing
adjacency or incidence between these entities. An iterated line graph arises from the repeated application
of the line graph construction, where each iteration takes the previous line graph as its input. Similarly, an
iterated total graph is generated by iteratively applying the total graph transformation a specified number of
times. This paper investigates the hypergraph and superhypergraph analogues of these constructions, providing
a foundation for further theoretical development.

A Mathematical Models to Study the effects of Biocontrol on the Dynamics of Tomato Bacterial Wilt Disease

Saminu Bala — 2025-12-31

Tomato farmers are faced with many challenges such as the presence of Tomato bacterial wilt disease (TBWD) caused by Ralstonia solanacearum (RS) bacterium. The congeneric strain of this bacterium called Ralstonia pickettii (RP) is harmless to tomatoes and is known to compete with RS for space and resources. We formulated models to investigate the conditions under which TBWD can be controlled by incorporating RS and the populations of RP as biocontrol using both ordinary and stochastic differential equations, assuming that the model parameters depend on climatic conditions. We investigated the basic properties of the model and the existence and stability of steady states. We find that biocontrol alone can only suppress TBWD but cannot eradicate it; RS and RP can coexist even when the reproduction number is less than unity, implying that the disease will persist. Sensitivity analysis conducted indicates that the rate at which RP consumes the resources of RS is the most sensitive parameter affecting the reproduction number. Increasing the value of this parameter will have more meaningful impacts in reducing the menace of TBWD. The numerical simula tions conducted indicate that the reproduction number alone cannot be used to establish the condition for eradication of the disease.

Modeling Health Risks Associated with Second-hand Tobacco Smoke Exposure

Clement Bahati Matogwa — 2025-12-31

A non-smoker who is exposed to second-hand tobacco smoke is in danger of suffering from diseases such as coronary heart disease, asthma attacks, stroke and lung cancer. This exposure occurs in various set tings, including living with smokers at home, visiting bars and casinos, public places, and transport vehicles. Additionally, individuals exposed to second-hand tobacco smoke may experience severe health risks includ ing deaths. To gain insights about the dynamics of second-hand tobacco smoke exposure and its associated health risks to non-smokers, a deterministic mathematical model is developed and analysed. Such a model is developed by using non-linear first order ordinary differential equations and the analysis was carried out ana lytically and numerically. Numerical simulation results in this study confirm that, 90% increase in interaction between smokers and non-smokers can increase health risks to non-smokers by 7%. Additionally, the formu lated system exhibits backward bifurcation implying the possibility of having large outbreaks of health risks related to second-hand tobacco smoke even in communities with a relatively small number of smokers. The study underscores the importance of interventions to mitigate the health risks associated with second-hand tobacco smoke. Specifically, efforts should focus on reducing interactions between smokers and non-smokers during smoking or providing robust support mechanisms to help smokers quit.

TRANSMISSION DYNAMICS OF CHOLERA DISEASE USING FRACTIONAL--ORDER MODEL

Frankline Eze — 2025-12-31

Traditional epidemic models usually use integer-order derivatives, which often fail to capture inherent memory and hereditary effects involved in the transmission of diseases. This work presents a cholera model of fractional order that is formulated within the Atangana–Baleanu fractional derivative, which possesses a non-local and nonsingular kernel. The existence and uniqueness of the proposed model were analyzed uti lizing Banach’s and Krasnoselskii’s fixed point theorems, while the stability analysis results indicated that the disease-free equilibrium of the model is locally asymptotically stable if the basic reproduction number is less than unity. Numerical simulations are presented using the predictor–corrector scheme in the Atan gana–Baleanu framework, showing the significant impact of the fractional order on the system dynamics. Our results suggest that the memory-dependent transmission patterns exhibited by cholera are captured more exactly by the fractional-order formulation than its classical integer-order counterpart. Overall, this paper confirms the mathematical flexibility and improved realism of the Atangana–Baleanu fractional oper ator within the context of modeling cholera dynamics and further advances the theoretical developments underlying fractional epidemic modeling.