Mathematical Modelling and Analysis of Malaria Transmission Dynamics among Children under Five with Early and Late Treatment Interventions | Chapter 2 | Mathematics and Computer Science: Research Updates Vol. 7

 

Malaria, a life-threatening disease caused by Plasmodium parasites transmitted through the bites of infected Anopheles mosquitoes, poses a persistent public health challenge in Nigeria due to its complex transmission dynamics. Mathematical modeling provides a robust framework to unravel the complexities of malaria transmission, enabling predictions of disease dynamics and evaluation of control measures. This study develops a compartmental SEIIR-SEI model to evaluate the impact of early (λ1) and late (λ2) treatment interventions on malaria transmission among children under 5, aiming to guide effective control strategies. Parameterized with Nigerian malaria case data (2007–2021), the model integrates human and mosquito populations to examine how treatment timing affects the basic reproduction number (R0) and disease prevalence. The methodology encompasses model formulation, assumptions, parameter estimation, analytical methods, and numerical simulations. Using stability analysis, sensitivity analysis, and numerical simulations, we find a baseline R0 = 2.24, indicating endemicity. Early treatment reduces this to R0,λ1 = 1.46, outperforming late treatment (R0,2 = 1.65). Sensitivity analysis highlights mosquito biting rates ((b) and λ1 as key drivers of R0. Simulations show that 60–80% early treatment coverage (λ1 ≥ 0.6) within 24 hours significantly lowers prevalence within 120 days, unlike 100% late treatment (λ2 = 1.0). The disease-free equilibrium is stable when R0 < 1, achievable with high λ1. Rapid diagnosis, Artemisininbased Combination Therapies, and vector control are critical for eradication. Policymakers should enhance healthcare access and surveillance to reduce Nigeria’s malaria burden. These findings provide a rigorous, data-driven foundation for policymakers to optimize malaria control programs, reducing morbidity, mortality, and economic burdens in endemic regions. Future studies should explore fractionalorder models or spatial dynamics to further refine intervention strategies.

 

Author(s) Details

 

D.B. Opaginni
Department of Mathematical Sciences, University of Abuja, FCT, Nigeria.

 

M.O. Durojaye
Department of Mathematical Sciences, University of Abuja, FCT, Nigeria.

 

Please see the book here :- https://doi.org/10.9734/bpi/mcsru/v7/6198

Study of Thermovibrational Convection in a Fluid Saturated Porous Medium | Chapter 12 | Exploration of Knowledge and Information in Sciences

The investigation delves into the intriguing realm of fluid dynamics, specifically exploring the influence of gravity modulation on the onset of convection in a horizontal fluid saturated porous layer subject to bottom heating. In this scenario, the flow through the porous layer is governed by an extended form of Darcy’s law incorporating Brinkman’s boundary layer correction. Through a comprehensive stability analysis utilizing the method of small perturbations and employing normal mode analysis, the study endeavors to unravel the intricate interplay between gravity modulation and convection onset. To tackle this complex problem the study harnesses the power of Mathieu’s functions, renowned for their utility in describing periodic phenomena in various scientific disciplines. Central to the investigation is the concept of instability and its manifestation through synchronous and subharmonic modes. Instability represents a critical threshold in system’s behaviour, marking the point at which small perturbations can lead to

significant deviations from initial state. By elucidating the mechanisms governing instability and transition phenomena, the study lays ground work for future research aimed at harnessing these phenomena for practical applications.

 

Author (s) Details

R.K.Brinda
Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamil Nadu, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mono/978-93-48859-02-0/CH12

Stability-Preserving Stochastic Perturbations | Book Publisher International

The stability of equilibria is a topic of importance in mathematical models in many branches of science. Since systems generally do not start in equilibrium states, the equilibria of chief scientific interest are those which are attracting, in the sense that the system converges to these equilibria over time. Perhaps the simplest mathematical model which captures this is a deterministic differential equation, and we can study the long-time behaviour of the solution of the equation.

Such simple models, however, may underplay the role that randomness may play in the evolution of the system. The character of the stochastic disturbance may be of many types: one type, which this considers, is when the intensity of the random term is independent of the state of the system, but varies over time. This models persistent stochastic shocks. The question now is: which (possibly fading) time-varying intensities of the shock preserve the stability of the system, and which render the equilibrium unstable. The book seeks to answer this question for one-dimensional linear (and possibly) nonlinear differential equations in a very comprehensive manner. The book involves stochastic calculus (mainly stochastic differential equations), and also some ideas from the theory of differential equations which we will study. According to the writers’ interest, one can ask whether numerical simulations of the stochastic equation preserve the asymptotic behaviour of the original continuous-time problem. The research outcome is most relevant to Probability and Finance (as well as Simulation for Finance, if numerical studies are involved) as well as Ito calculus.

This book is concerned with the study of linear differential and difference equations which are subjected to an outside force. Any equation without any External force is considered to be “stable “in a sense we make precise below.

The question we address is: what are precisely the conditions on this external force for which this stability is preserved, and if these conditions are not satisfied, what then is the long–time behaviour of the solution?

The stochastic differential equations (SDEs) driven by Brownian motions have been attracting lots of attentions. When some unexpected events happen, some jumps may be needed to model the effects of those events. For example, the out break of a new disease can cause the National Economy have some instability in the country. To take both the continuous and discontinuous random effects into consideration, SDEs driven by both Brownian motions and Poisson jumps are often employed as a generalisation of the SDEs only driven by Brownian motions. Despite the wide applications, the explicit solutions to SDEs are hardly found. Therefore, to construct some efficient numerical methods is of great importance.

In general, we are able to characterise whether the solution has retained its stability, or whether the solution remain under control, but is not convergent, or whether the solution become unbounded.

Author(s) Details:

Dr. Miya Nakazwe Hoyer,
Department of Financial Mathematics, Dublin City University, Republic of Ireland.

Prof. John Appleby,
School of Mathematical Sciences, Dublin City University, Republic of Ireland.

Please see the link here: https://stm.bookpi.org/SPSP/article/view/13328

Effect of Viscosity in Brane-World| Chapter 12 | New Frontiers in Physical Science Research Vol. 2

 In the Randall-Sundrum type II (RS) brane-world model with or without the Gauss-Bonnet (GB) factor and in the presence of an imperfect fluid, I provide a precise cosmological solution. In this scenario, I take into account both the power law and exponential models of the early cosmos. The Truncated Israel-Stewart (TIS) hypothesis of viscosity is used to create cosmological models. It is discovered that during the GB regime, the influence of viscosity accelerates the universe's pace of expansion. Additionally, I investigate the stability of the dynamical system equilibrium points related to the evolution of the viscous fluid in the RS Brane with or without a GB term.

Author(s) Details:

Dilip Paul,
Department of Physics, Islampur College, Islampur, Uttar Dinajpur, West Bengal, India.

Please see the link here: https://stm.bookpi.org/NFPSR-V2/article/view/8211

Investigating the Stability Analysis of a Mathematical Model for Awareness Initiatives on Registration of Persons in Kenya| Chapter 10 | Current Topics on Mathematics and Computer Science Vol. 9

The stability analysis of a mathematical model of awareness initiatives in person registration in Kenya is discussed in this research. A mathematical model is built using Ordinary Differential Equations to assess the efficacy of print, electronic, and word-of-mouth media in disseminating registration information. To ensure that the model is mathematically meaningful, positivity and boundedness of solutions are established. The Next Generation Matrix is used to calculate the Basic Reproduction number R0. We show the maximum awareness equilibrium as well as the awareness free equilibrium. The model's stability analysis shows that the Awareness free equilibrium is both locally and globally asymptotically stable when R0 1, indicating no spread of awareness, and unstable when R0 > 1, indicating information spread in the population, whereas MAE is locally asymptotically stable when R0 > 1, indicating information spread in the population.

Author (S) Details

Ann N. Mwambia

Chuka University, Kenya.

Mark O. Okongo

Chuka University, Kenya.

Gladys G. Njoroge

Chuka University, Kenya.

View Book :- https://stm.bookpi.org/CTMCS-V9/article/view/3642