Journal of Mathematical Analysis and Modeling

Mpox transmission dynamics: A mathematical modeling approach with bifurcation analysis of control interventions

2025-09-23T11:59:07+00:00

A new nonlinear mathematical model of Mpox epidemic, encompassing any of the fea- sible interactions that provide the virus transmission in the population has been analyzed. The model involves vaccination, quarantine, and hospitalization as critical control interven- tions, emphasizing the influence of prompt quarantine strategy in preventing the spread of Mpox disease. The model identifies three endemic equilibria besides the Mpox-free equilib- rium. Moreover, the local and global stability of the equilibria are examined with respect to a basic reproduction rate. Furthermore, the model admits a backward bifurcation at a threshold parameter. At the same time, the method of proof yields sufficient conditions for the nonoccurrence of said phenomena, thereby enhancing the efficacy of prevention and supporting the eliminating of Mpox outbreaks.

Mathematical Modeling on Malaria Dynamics: Immunity, Reinfection, Drug Resistance, Treatment and Vector Control by Sensitization.

2025-09-17T07:14:56+00:00

Malaria is a serious public health issue that impacts a vast number of people worldwide. A mathematical model of malaria that included medication resistance, re-infection, immunity, intensive treatment, and vector control by sensitization was examined in order to address the dynamics of the disease. The Next Generation Matrix Method's Disease Free Equilibrium was used to analyze the model. It was discovered that when the fundamental reproductive number is smaller than one, the Disease Free Equilibrium is asymptotically stable both locally and globally; otherwise, it is unstable. Additionally, the Endemic Equilibrium was computed. Additionally, the endemic equilibrium's local stability was assessed. The Lyapunov function was used to analyze the Endemic Equilibrium point's global stability. The findings demonstrated that when the fundamental reproductive number is bigger than one, it is globally asymptotically stable; otherwise, it is unstable. Furthermore, the most vulnerable characteristics were shown by sensitivity analysis of the basic reproductive number. The findings indicated that rigorous treatment lowers the infectious curve and that vector control sensitization should be implemented to lower malaria infections. The Ministry of Health will benefit from this study since it will help raise awareness about vector control by advising people to use treated mosquito nets, and apply insecticide to prevent mosquito bites, which will reduce the number of malaria infections. Additionally, it assists policymakers and the government in making sure that people in areas where malaria is endemic are aware of the importance of vector management.

A MATHEMATICAL MODEL FOR THE DYNAMICS OF COVID-19 AND MONKEYPOX CO-INFECTION CONSIDERING THE EFFECTS OF VACCINATION, QUARANTINE, AND REINFECTION

2025-12-29T20:30:40+00:00

A deterministic compartment model for the co-infection of COVID-19 and Monkeypox taking into account vaccination, quarantine, treatment, and reinfection is introduced. It is demonstrated that the compartment model is mathematically well-posed. The disease-free equilibrium and local stability are obtained. The basic reproduction number $R_0$ is determined. The global stability result for the disease-free equilibrium is proven using the Castillo-Chavez and Song method. A Lyapunov function is introduced based on which it establishes global stability for endemic equilibrium. A critical modifying variable, $\eta [0,1].$ denoting the efficacy of treatment per session against mortality, is explored. Simulation outcomes indicate that low $\eta$ (i.e when $\eta = 0$, there is Effective treatment) decreases mortality but enhances long-term treatment efforts, and high $\eta$ (i.e when $\eta = 1$, there is Ineffective treatment) deteriorates survival rates among the treated category. Results obtained from subsequent simulations indicate that COVID-19 exerts a postponing effect on Monkeypox infections due to its influence on enhancing the reproduction number and boosting co-infections.
These findings bring out the need to incorporate vaccine, quarantine, and treatment against dual outbreaks of Covid-19 and Monkeypox.

Some new Gronwall-Bellman and Bihari type integral inequalities and its applications to Riemann-Liouville fractional differential equations

2025-11-13T10:52:10+00:00

In this work, we establish new variants of Gronwall–Bellman type and Bihari type integral inequalities, which serve as generalizations of some classical inequalities as well as weakly singular integral inequalities. These results provide efficient analytical tools for the qualitative study of solutions to fractional differential equations. In particular, we investigate nonlinear fractional Cauchy problems involving the Riemann–Liouville fractional derivative. Using an equivalent Volterra-type integral equation of second kind of the Cauchy problem, we analyze the dependence of solutions on initial conditions and nonlinear terms.

Conformal changes of bisymmetric and birecurrent Finsler Spaces with a generaliezd Cartan connection

2025-09-07T19:05:58+00:00

The aim of this article is to study the conformal changes in special Finsler Spaces. In particular, we consider bisymmetric and birecurrent Finsler Spaces that are conformal to each other. Several results concerning these spaces have been established in this work

On a novel n-tuple variable order q-fractional derivative with respect to ψ function: hybrid difference equation and the well-posedness of the solution

2025-11-16T00:39:16+00:00

This paper introduces a novel generalized fractional operator: the n-tuple variable-order
q-fractional derivative with respect to a ψ function. This operator extends and unifies
several existing q-fractional operators, including the Riemann–Liouville, Caputo, and Hilfer
types, together with their variable order variant and ψ-dependent variant. Fundamental
properties and related results are established to analyze the well-posedness of hybrid
fractional difference equations. The existence of the solution is proved via Krasnoselskii’s
fixed point theorem, while uniqueness is demonstrated using the Banach contraction
principle. Furthermore, the Ulam–Hyers stability of the solution is investigated. Also, an
example is presented to illustrate the result.