On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells by Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel

“…The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. …”
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Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays by Fulgensia Kamugisha Mbabazi, Joseph Y. T. Mugisha, Mark Kimathi

“…The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratio R0 is less than unity and unstable otherwise. …”
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Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model by Fabien Crauste

“…We analyze the asymptotic stability of a nonlinear system of two differential equations with delay,describing the dynamics of blood cell production. …”
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Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument by Kuo-Shou Chiu

“…Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. …”
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Solving arbitrary one-loop reduction via generating function by Tingfei Li, Yuekai Song, Liang Zhang

“…We first establish the partial differential equations governing the higher-pole generating function. …”
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Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method by E. H. Doha, W. M. Abd-Elhameed

“…The proposed algorithms are extended to solve the two-dimensional sixth-order differential equations. A family of symmetric generalized Jacobi polynomials is introduced and used as basic functions. …”
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Analysis of SI models with multiple interacting populations using subpopulations by Evelyn K. Thomas, Katharine F. Gurski, Kathleen A. Hoffman

“…Computing endemic equilibria and basic reproductive numbers for systems of differential equations describing epidemiological systems with multiple connections between subpopulations is often algebraically intractable. …”
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The Quantum Analysis of Nonlinear Optical Parametric Processes with Thermal Reservoirs by Tamirat Abebe, Nebiyu Gemechu, Chimdessa Gashu, Kebede Shogile, Solomon Hailemariam, Shimelis Adisu

“…In this paper, employing the stochastic differential equations associated with the normal ordering, the quantum properties of a nondegenerate three-level cascade laser with a parametric amplifier and coupled to a two-mode thermal reservoir are thoroughly analyzed. …”
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Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes by Xiongwei Liu, Junjun Xu, Xiao Wang, Lizhi Cheng

“…This paper investigates two methods of releasing transgenic mosquitoes and proposes two epidemic models involving malaria patients, anopheles, wild mosquitoes, and transgenic mosquitoes based on system of continuous differential equations. A basic reproduction number R0 is defined for the models and it serves as a threshold parameter that predicts whether malaria will spread. …”
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Analytical approach to explore theory of creeping flow with constant absorption by Abdul M. Siddiqui, Q.A. Azim, Getinet A. Gawo, Ayesha Sohail

“…The stream function is used to transform the governing equations to system of ordinary differential equations. The analytical solutions are found for velocity components, pressure distribution, the axial flow rate, the mean pressure drop and the shear stress. …”
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Analysis of the Financial Chaotic Model with the Fractional Derivative Operator by Mamadou Diouf, Ndolane Sene

“…Numerical discretization for the fractional differential equations is applied to the chaotic financial model described by the Caputo derivative. …”
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Dynamics of a plant-herbivore model with toxin-induced functional response by Ya Li, Z. Feng

“…Themodel consists of three ordinary differential equations describingone herbivore population and two plant species with differenttoxicity levels. …”
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Stability Analysis of Pneumatic Cabin Pressure Regulating System with Complex Nonlinear Characteristics by Xinhua Zheng, Lili Xie, Lizhuo Liu

“…The governing equations of the considered system consist of 8 differential equations. In the circumstance, commonly used methods of nonlinear system analysis are not applicable. …”
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An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges by Xue Kai, Wang Jiufa, Li Qiuhong, Wang Weiyuan, Wang Ping

“…The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. …”
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Raves, clubs and ecstasy: the impact of peer pressure by Baojun Song, Melissa Castillo-Garsow, Karen R. Ríos-Soto, Marcin Mejran, Leilani Henso, Carlos Castillo-Chavez

“…In this study, a system of differential equations is used to model the peer-driven dynamics of ecstasy use. …”
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Mathematical Modelling of Malaria Disease Transmission and Control. by Muhangi, Benard

“…The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. …”
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On the Regularity of the Entropy Solution of the Fractional-Semigeostrophic Equation Using Ultrafilters by Gilles Tamba Bokolo

“…This work lays the groundwork for future studies on fractional partial differential equations in geophysical contexts, potentially leading to more accurate predictive models in meteorology and oceanography.…”
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Mathematical Model for Thermal Processes of Single-Core Power Cable by D. I. Zalizny, S. N. Prohorenko

“…Thermal processes between homogeneous bodies are described by a system of four differential equations. The paper contains a proposal to solve this system of equations with the help of a thermal equivalent circuit and the Laplace transform. …”
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Computational Modelling of Blood Flow Development and Its Characteristics in Magnetic Environment by Gopal Chandra Shit

“…The governing coupled nonlinear differential equations of magnetohydrodynamic (MHD) fluid flow are reduced to a nondimensional form, which are then characterized by four dimensionless parameters. …”
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Topology in nonlinear extensions of hypernumbers by M. S. Burgin

“…Modern theory of dynamical systems is mostly based on nonlinear differential equations and operations. At the same time, the theory of hypernumbers and extrafunctions, a novel approach in functional analysis, has been limited to linear systems. …”
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