International Journal of Mathematical Sciences and Optimization: Theory and Applications

Optimal Investment Strategy With Currency Uncertainty

I. Adinya — 2025-07-30

Currency uncertainty, characterized by fluctuations in exchange rates, significantly impacts the valuation of investments and the timing of investment decisions. This paper develops a real options framework incorporating a novel currency uncertainty ratio to capture the impact of exchange rate fluctuations on investment timing. We analyze two cases: (i) project value following a geometric Brownian motion (GBM) with a constant investment cost and (ii) both project value and investment cost evolving as GBMs. Using stochastic control and optimal stopping theory, we derive closed-form solutions for the investment thresholds and option values. We further conduct a sensitivity analysis to explore how investment thresholds respond to changes in currency risk, volatility, and discount rates. Our results suggest that currency uncertainty significantly influences investment timing, often delaying investment decisions. These findings have important implications for multinational corporations, policymakers, and financial analysts concerned with investment under foreign exchange risk.

Some New Operations on Picture Fuzzy Multisets

T. O. Sangodapo — 2025-07-30

A multiset is an extension of a crisp set in which elements are allowed to occur more than once, enabling the representation of data where frequency or multiplicity is essential. Building upon this, fuzzy multisets introduce a degree of membership to each element, capturing both quantity and uncertainty. Further developments have led to the formulation of picture fuzzy multisets a robust framework that extends picture fuzzy sets. In this paper, we propose some new operations on picture fuzzy multisets by analyzing existing operations on fuzzy sets, and fuzzy multisets, extending these foundations using picture fuzzy logic principles to define operations that maintain the consistency of positive membership, neutral membership, and negative membership and refusal degrees, establishing a set of axioms and properties (such as commutativity, and distributivity) that the operations must satisfy, proving theorems that verify these properties and constructing a detailed numerical example to illustrate and validate the behavior and correctness of the proposed operations. It was shown that the proposed operations are well-defined, internally consistent, and closed under the structure of PFMs. The example demonstrates that the operations handle ambiguity, contradiction, and repetition effectively, making them suitable for applications in multi-criteria decision-making, knowledge representation, and information systems. The new operations significantly broaden the mathematical toolkit available for handling picture fuzzy multisets. They lay a foundation for future research into more complex structures such as picture fuzzy multirelations, aggregation operators, and soft computing models based on picture fuzzy multisets.

Eight-Order Implicit Block Method With Two Off-Step Points for Stiff Ordinary Differential Equations

C. N. Abhulimen — 2025-08-31

In this work, we derived eight-order, implicit block formula using backward differentiation method with two off-step points for solving stiff ordinary differential equations. We solve some standard set of stiff initial value problems (IVPs) using the new method. We then compared the numerical results with the existing methods which have solved the same set of ivps. We have also verified the consistency, order and stability of the method whereby, method is found to be A-stable and consistent.

Testing Homeostasis Using the Designed Matlab GUI of Cardiovascular-Respiratory System Mathematical Model

E. Nyirishema — 2025-08-31

Homeostasis is the body's mechanism for maintaining internal stability amidst external changes, particularly within the cardiovascular and respiratory systems. This study applied optimal control problem strategies to sustain homeostasis by regulating key physiological parameters such as blood pressure, oxygen, and carbon dioxide levels. A stability analysis was conducted on a mathematical model of the human cardiovascular-respiratory system using a GUI in MATLAB App Designer to test this homeostasis. The findings demonstrated that the model's variables consistently averaged within normal physiological ranges, affirming the successful maintenance of homeostasis. The GUI provided intuitive and interactive graphical outputs, effectively distinguishing between healthy and unhealthy individuals. Stable outputs were observed in healthy subjects, while instability was evident in unhealthy subjects, underscoring the system's sensitivity to pathological conditions. The user-friendly interface efficiently managed input data and delivered precise health status indicators. The model reliably simulated the impact of various disease parameters, with variables remaining within normal ranges in healthy scenarios and deviating in the presence of disease, thereby highlighting its potential as a valuable tool for clinical and research applications.

On Enriched Weakly Contractive Maps in Hilbert Spaces

O. T. Wahab — 2025-09-30

This paper introduces a class of enriched weakly contractive mappings for approximating a non-Picard average operator on a closed convex subset of Hilbert spaces. By imposing the enriched weakly mapping on the average operator, we establish and prove some results concerning convergence theorems (strong and weak), stability, and convergent rate. The validity and generality of the new class of enriched weakly mappings are examined with the aid of practical examples. The results harmonize and improve some recent results on enriched contractive-type mappings.

A Fourth-Order Compact Finite Difference Scheme for First Order Initial Value Problems

S. O. Imoni — 2025-10-05

In this paper, a fourth order Compact Finite Difference Scheme(CFD) for the numerical solution of first order initial value problems (IVPs) of Ordinary Differential Equations (ODEs) is discussed. Compact finite difference scheme is a class of numerical methods that are particularly designed for solving Partial Differential Equations (PDEs). However, in this paper, we consider the compact finite difference scheme for approximating the numerical solution of ordinary differential equations. The application of this scheme enables the solution of first-order ODEs across all grid points in just one computational sweep (single iteration), rather than requiring repeated iterative updates. Numerical examples have been included to demonstrate the accuracy of the scheme and Numerical results compared with the exact solution and other existing methods from recent literature. The scheme is shown to be efficient for the numerical integration of first order differential equations.

Quantifying the Public Health Effects of Vaccine Hesitancy and Delays in Screening Clinically Infected Patients: Insights From a COVID-19 Transmission Model

Paride O. Lolika — 2025-10-10

Motivated by the recent COVID-19 outbreak, we develop a time delay infectious disease model that incorporates vaccination and screening of clinically infected patients and calibrate it using Chinese data to understand the quantitative implications of vaccine hesitancy and delay in the screening of clinically infected patients. Vaccine hesitancy refers to the denial or delay in acceptance of vaccines despite their availability. Understanding the implications of vaccine hesitancy is therefore essential for designing public health interventions. Analysis of the model revealed that whenever $R_{0} \leq 1$ , there exists a globally asymptotically disease-free equilibrium. However, whenever $R_{0} > 1$ , there exists a unique endemic equilibrium which is globally asymptotically stable. In addition, results also show that vaccine hesitancy and delay in hospitalizing clinically infected patients have a stronger impact on the deaths toll and new infections generated. Vaccine hesitancy and delayed screening of clinically infected patients lead to harmonic oscillations in deaths and new cases, which, however, die out over time. Our findings underscore the importance of including vaccine hesitancy and delay in hospitalizing clinically infected patients in the design of control strategies for infectious diseases.

An Inventory Model for Non-Instantaneous Deteriorating Items Under Two-Phase Demand and Two-Level Trade Credit

Z. H. Aliyu — 2025-10-15

Trade credit is widely used in modern business transactions as it provides alternative to price reduction, encourage retailer's demand and minimizes holding cost. In this study, an inventory model for non-instantaneously deteriorating items under trade credit is developed. The demand is in two-phase, in the first phase, when there is no deterioration, the demand is stock dependent due to freshness of the stocked items whereas in the second phase, when deterioration sets in, the demand is assumed to be price dependent as a result of reduction in quality of the product. Profit functions of the model was obtained. The necessary and sufficient conditions for the existence and uniqueness of the optimal solutions to the profit functions was established. The Newton-Raphson iterative method was employed to find the solutions to the numerical examples using MATLAB. Sensitivity analysis was carried out to test the sensitivity of the model's parameters on the model. The major findings reveal that the holding cost, deterioration cost and the interest charged rate significantly influence the optimal cycle period and the maximum total profit.

On Some Properties of Quantum Stochastic Multivalued Operators

L. A. Abimbola — 2025-10-15

This paper explores the properties of multivalued maps associated with quantum stochastic operators as formulated by Hudson and Parthasarathy. We focus on key aspects including the measure of noncompactness, continuity of multivalued operators, and the condensing property. Also, we consider measurability, strong measurability, the Castaining representation, and the Lusin property. These findings contribute to a deeper understanding of the behavior of multivalued operators in quantum stochastic analysis and highlight the interconnectedness of these properties within the framework of quantum stochastic analysis. By investigating this properties, our work provides valuable insights that could inform future research and enhance the theoretical foundation of quantum stochastic processes.

Understanding the Dynamics of Amebiasis Using Mathematical Modelling Approach: Optimal Control Strategies and Cost-Effectiveness Analysis

K. A. Tijani — 2025-10-15

Amebiasis is a parasitic infection of the intestine caused by the amoeba Entamoeba histolytica and is endemic in tropical countries with poor sanitation and hygiene. To explore the dynamics of amebiasis and identify effective control interventions, a mathematical model is developed. This model incorporates a treatment class within the human population and accounts for the concentration of the amebiasis pathogen in the environment. The study derived the steady states, stability, and the basic reproduction number of the infection. A global sensitivity analysis is also conducted to identify the most significant parameters influencing the disease's spread. Subsequently, an optimal control model is formulated, featuring four time-dependent controls: hygiene practices, efficient screening of infected individuals, effective treatment, and disinfection/sterilisation of the environment. This model is analysed and simulated across four categories—single, double, triple, and quadruple combinations—to assess the impact of these control measures. Additionally, a cost-effectiveness analysis is conducted using the incremental cost-effectiveness ratio (ICER) method. The findings provide valuable insights that can help policymakers effectively control the disease while managing limited resources. The results indicate that any control combination that includes efficient screening of infected individuals is the most cost-effective strategy for reducing amebiasis in society. However, in a single case where resources are limited, Strategy 2 - efficient screening of infected individuals - emerges as the most cost-effective method for eradicating the disease. With additional resources, the most effective double-combined control strategy for disease eradication is Strategy 8, which combines Strategy 2 with efficient treatment. For the triple control strategy, the most cost-effective control Strategy is Strategy 14, which integrates Strategy 8 and disinfection/sterilisation of the environment. However, the overall most cost-effective strategy remains Strategy 2.