This paper presents an analytical approach for Black-Scholes European options model in the sense of powered modified log-payoff functions. This approach is based on the reduced differential transform method (RDTM). The solutions are obtained by using RDTM. The techniques involved are simple, easy, and adaptable, without sacrificing accuracy. With less computational time, the desired explicit solutions are obtained. As a result, it is assumed that the assets are driven by geometric Brownian motion and do not pay dividends.

Solow Growth Model (SGM) is an economic model that is exogenous in nature and examines the relationship between the output and input levels in an economy over a period of time. It projects long-term economic growth in relation to labour (population growth), savings rate, and technological development. However, traditional approaches to solving the Solow growth model may rely on complex mathematical techniques that might not give an accurate representation of real-world economic dynamics. Thus, this paper applies the Natural Decomposition Method (NDM) to the Solow growth financial model. The NDM is a numerical technique that combines the Natural Transform (NT) and the ADM-Adomian decomposition method. The NDM simplifies problem-solving by converting the original differential equations into algebraic equations as regards limitations associated with nonlinear models. From the results obtained by applying the NDM to the Solow growth financial model, researchers and policymakers can better understand the interplay between financial variables, such as savings rates, investment, and capital allocation, and their impact on economic growth dynamics, as a systematic approach to capturing the complex relationship between finance and economic development within the Solow framework is ensured. Further research and application of the NDM can contribute to advancing the knowledge of economic dynamics and support evidence-based decision-making in economic policy.

Deposit insurance is a mechanism by which financial institutions are stabilized. The danger of a bank’s inability to meet its consumer commitments due to its suspended license is insured through deposit insurance practices. A flat-rate insurance scheme would contribute to moral hazard and a financial panic when banks indulge in dangerous practices. Hence, a reliable model with an explicit solution is required. This paper considers a risk rate model for deposit insurance engendered by the classical Black Scholes Option Pricing Model. The solutions are obtained via the application of Banach Contraction Mapping or Method. The procedures involved are straightforward, easy, and flexible, even without giving up accuracy. The desired explicit solutions are obtained with less computational time.

Malaria importation is one of the hypothetical drivers of malaria transmission dynamics across the globe. Existing studies that focused on malaria importation used mobile phone data to study human mobility trends in relation to malaria incidences but did not capture the mobility patterns of those in the human population who do not use a mobile phone based on institutional restriction policy. Hence, the purpose of this study is to assess the impact of human mobility on malaria transmission dynamics using Covenant University Undergraduate Students in Nigeria who are restricted from mobile phone usage as the pilot population study group. One of the core objectives of this study was to develop a novel location-specific Internet Data Model (IDM) to conceptually express travel rates among the pilot population study group of interest. Furthermore, this work statistically modeled the association between IDM-derived travel and hospital-reported malaria incidences.

Malaria importation is one of the hypothetical drivers of malaria transmission dynamics across the globe. Several studies on malaria importation focused on the effect of the use of conventional malaria control strategies as approved by the World Health Organization (WHO) on malaria transmission dynamics but did not capture the effect of the use of traditional malaria control strategies by vigilant humans. In order to handle the aforementioned situation, a novel system of Ordinary Differential Equations (ODEs) was developed comprising the human and the malaria vector compartments. Analysis of the system was carried out to assess its quantitative properties. The novel computational algorithm used to solve the developed system of ODEs was implemented and benchmarked with the existing Runge-Kutta numerical solution method. Furthermore, simulations of different vigilant conditions useful to control malaria were carried out. The novel system of malaria models was well-posed and epidemiologically meaningful based on its quantitative properties. The novel algorithm performed relatively better in terms of model simulation accuracy than Runge-Kutta. At the best model-fit condition of 98% vigilance to the use of conventional and traditional malaria control strategies, this study revealed that malaria importation has a persistent impact on malaria transmission dynamics. In lieu of this, this study opined that total vigilance to the use of the WHO-approved and traditional malaria management tools would be the most effective control strategy against malaria importation.

People deal with the complexities of uncertain data; the most effective method for coping with uncertainty is the fuzzy set theory (Uncertain Sets) developed by Zadeh in 1965. This paper proposes a method to examine Sanchez’s medical diagnosis approach using Fuzzy Soft Complement in addition to a matrix representation of Fuzzy Soft Collection. Medical data from a particular hospital in Lagos, Nigeria, were collected and tested for diarrhea, cholera, and dysentery.

This research aims at profit maximization and loss minimization in any FX market trading. A geometric progression (geometric sequence), is said to be a non-zero number progression or sequence in which each term following the first is obtained via multiplying the prior by the common ratio, which is a predetermined non-zero value. This method seeks to open an opposite position to an existing initial position in order to hedge that initial position in the event that the market moves against our trade. There are a number of mathematical models to develop new hedging strategies for Forex trading. Due to the apparent high level of unpredictability in price movement, forecasting the future of a stock price is a challenging endeavor. The research would like to study one with geometric progression in particular. In other words, every number can be entered as multiple integer of a different number. Thus, 1, 2, 4, 8,..., 2n is a step forward. Smart traders never take more risks than their capital, however, the otherwise is viewed and considered here.

Despite concerted efforts by the World Health Organization (WHO) to control malaria, it is still being diagnosed in patients visiting hospitals in Tropical Countries of the World. Hence, this study investigated the risk factors responsible for malaria transmission dynamics through a hospital case study. Data of patients that presented with malaria from June 2019 to December 2020 were acquired from Covenant University Medical Centre in Ota, South West Nigeria. Descriptive statistical analyses were carried out so as to examine the factors associated with malaria incidence rate such as age, gender and travel history using the R programming platform. 14% of the total outpatient visits from June 2019 to December 2020 presented with malaria. Furthermore, the mean of the ages of those that presented with malaria, was 23.10 whereas the median of their ages was 22.0. Out of the total malaria cases, 57.7% were males whereas 42.3% were females. Results also showed that there was a significant positive correlation between malaria and travel. In conclusion, it is recommended that malaria control policy formulators should focus on the most vulnerable group of individuals as identified in this study. Further, more efforts should be geared towards curbing malaria importation as a result of human travel, by the different health authorities across the globe.

In this study, the modified Picard Iterative Method (MPIM) is used to provide analytic and numerical solutions to linear Schrödinger Equations. These approximate-analytical solutions for the examples under consideration are easily computed. The suggested method is employed without any transformation, discretization, linearization, or limiting assumptions. The obtained results are similar to their exact forms. As a result, the approach is highly suggested for both linear and non-linear time-space fractional partial differential models with applications in various applied disciplines.

A new approach called the Generalised Picard Iteration Sch eme (GPIS) is used to solve the Navier-Stokes equations in this paper. The solutions are organized in a series with components that are readily computed. Because it delivers the exact solution to the solved issue with minimal computing effort while retaining a high degree of accuracy, this method appears to be extremely adaptable, efficient, effective, and dependable. It is not necessary to identify Lagrange multipliers. As a result, the presented method is recommended for dealing with higher-order linear and non-linear models.

Most of the real-life problems experienced in the industry these days cannot be expressed as a single differential equation but as a system of differential equations. Such structures of linear partial differential models are considered in this work with the aid of the Laplace Adomian decomposition method (LADM) in terms of solutions. Various examples are taken into consideration. The results are easily obtained, are in good agreement when compared to their exact forms. In addition, the proposed method seems effective and efficient; the solutions are graphically presented.

The Successive Approximation Method (SAM) is introduced in this research to solve the evolution equations. These approximate-analytical solutions of the considered cases are computed with ease. The proposed technique is used directly, without transformation, discretization, linearization, or any restrictive assumptions.

In this paper, Hybrid Block Adams Moulton Methods for step number k = 2 merged with two and three off-grid points were obtained and implemented in solving first order delay differential equations without the use of interpolation condition in evaluating the delay expression. The discrete schemes of these off-grid hybrid block methods were assessed through the continuous development of the linear multistep collocation method using a matrix conversion formula. The results obtained after the implementation of the proposed method in for numerical experiment of some first-order DDEs, the BHAMM2 schemes performed better and faster in satisfying the axioms for convergence and region of absolute stability than the BHAMM3 schemes at fixed step size z when examined with other existing methods.

Cryptography is an interdisciplinary topic that adopts concepts from several disciplines. In today’s environment, cryptography makes important use of computer science and mathematics, especially discrete mathematics. This study aims to discuss the daily use of matrices in cryptography. Globally, secure text communication is critical while various cryptosystems exist to accomplish this security. Hence, with regard to the cryptosystem, the key matrix from the plane’s equation is considered by determining the orthogonal matrix that implements reflection. This method boosts encryption security by making it more arduous to locate a secret key matrix. In order to produce encryptions, the approach uses the orthogonal matrix transform characteristics. The suggested encryption method’s simplicity enables it to be adapted to other circumstances requiring secret communication transmission

This study applies Elzaki Adomian Decomposition Method (EADM) to solve the Logistic Differential Model (LDM) of different forms and coefficients. Illustrative examples are considered, and the obtained results are in good agreement compared to those already in the literature. This study, therefore, recommends the proposed method (EADM) for application in other aspects of applied mathematics for real-life problems.

This paper aims at deriving apriori bounds on the gradient of positve solutions to a class of semilinear elliptic equation, with applications focusing on establishing a liouville type property for the bounded solutions of the Allen-Cahn equation on a complete noncompact Riemannian manifold with nonnegative Ricci curvature.

This paper applies the novel Successive Approximation Method (SAM) for the solution of the quadratic Logistic Differential Model (LDM). To confirm the reliability of the method, illustrative examples are considered, and it is remarked that the approximate-analytical solutions of the considered cases are computed with ease. The proposed technique is used directly, without transformation, discretization, linearization, or any restrictive assumptions.

The Successive Approximation Method (SAM) is introduced in this research to solve the non-homogeneous Gas Dynamic Equation (GDE). This GDE’s analytical solution is expressed via the SAM, in series form, with readily computed components. The proposed technique is used directly, without transformation, discretization, linearization, or any restrictive assumptions.

This paper proposes a fractional numerical study on Time-Fractional Barrier Option Model (T-FBOM) via highly convergence solution series method known as Homotopy Analysis Method (HAM). Furthermore, the pricing formula for T-FBOM was obtained. The performance of the method on some illustrative examples has been considered. The results obtained were compared with some existing approaches.

In the medical aspect of life, there are multiple ways of formulating a model that can be used to determine if a disease will become a pandemic or an epidemic. In this research, we discussed how we could use the numerical approach by applying the revised SEQIuIdRF (Susceptible, Exposed, Quarantined, Infected undetected, Infected detected, Recovered, and Failed) model to control or contain an infectious disease (COVID-19) by applying the effective contact rate. MATLAB software was used to solve the SEQIuIdRF model by considering population growth, mortality rate, infection rate, disease-induced death, failed treatment rate, and recovery rate, which gave pictographic diagrams of the increase and decrease of the infectious disease in the community.