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Applied Mathematics and Mechanics(English Edition) 2009年第3期30卷 373-380页

作者： oluwole daniel makinde Zhe-wei ZHOU Faculty of Engineering Cape Peninsula University of Technology P. O. Box 1906 Bellville 7535 South Africa 不详

This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy are obtained and solved by using a new computational approach based on a special type of Hermite-Padé approximation technique implemented in MAPLE. This semi-numerical scheme offers some advantages over solutions obtained with traditional methods such as finite differences, spectral method, and shooting method. It reveals the analytical structure of the solution function. Important properties of overall flow structure including velocity field, temperature field, thermal criticality, and bifurcations are discussed.

关键词： isothermal inclined plate third-grade fluid Hermite-Padé approximation thermal criticality

Optimal control analysis of hepatitis C virus with acute and chronic stages in the presence of treatment and infected immigrants

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International Journal of Biomathematics 2014年第2期7卷 141-163页

作者： Kazeem Oare Okosun oluwole daniel makinde Department of Mathematics University of TechnologyPrivate Bag X021 Vanderbijlpark 1900 South Africa Faculty of Military ScienceSteUenbosch University Private Bag X2 Saldanha 7395 South Africa

In this paper, we consider a deterministic hepatitis C virus （HCV） model and study the impact of optimal control on the screening of immigrants and treatment of HCV on the transmission dynamics of the disease in a homogeneous population with constant immigration of susceptibles. First, we derived the condition in which disease-free equilibrium is locally asymptotically stable and established that a stable disease-free equilibrium can only be achieved in the absence of infective immigrants. Second we investigated the impact of each control mechanism individually and the combinations of these strategies in the control of HCV. The costs associated with each of these strategies are also investigated by formulating the costs function problem as an optimal control problem, and we then use the Pontryagin＇s Maximum Principle to solve the optimal control problems. From the numerical simulations we found that the optimal combination of treatment of acute-infected and chronic-infected individuals control strategy produced the same results as the combination of the three strategies （combination of screening of immigrants, treatment of acute-infected and chronic-infected individuals）. By our model and these results, we suggest the treatment of acute-infected and chronic-infected individuals control strategy should be optimized where resources are scarce, because the implementation of the three strategies （combination of screening of immigrants, treatment of acute-infected and chronic-infected individuals） would imply additional cost.

关键词： Hepatitis C virus stability optimal control

Modeling Anthrax with Optimal Control and Cost Effectiveness Analysis

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Applied Mathematics 2020年第3期11卷 255-275页

作者： Shaibu Osman Dominic Otoo oluwole daniel makinde Department of Basic Sciences School of Basic and Biomedical Sciences University of Health and Allied Sciences Ho Volta Region Ghana Department of Mathematics and Statistics University of Energy and Natural Resources Sunyani Ghana Faculty of Military Science Stellenbosch University Saldanha South Africa

Anthrax is an infection caused by bacteria and it affects both human and animal populations. The disease can be categorized under zoonotic diseases and humans can contract infections through contact with infected animals, ingest contaminated dairy and animal products. In this paper, we developed a mathematical model for anthrax transmission dynamics in both human and animal populations with optimal control. The qualitative solution of the model behaviour was analyzed by determining Rhv, equilibrium points and sensitivity analysis. A vaccination class was incorporated into the model with waning immunity. Local and global stability of the model’s equilibria was found to be locally asymptotically stable whenever Rhv Rhv. It was revealed that reducing animal and human interaction rate, would decrease Rhv. We extended the model to optimal control in order to find the best control strategy in reducing anthrax infections. It showed that the effective strategy in combating the anthrax epidemics is vaccination of animals and prevention of humans.

关键词： Anthrax Model Stability Analysis Sensitivity Optimal Control Cost Effectiveness

A Review of the Mathematical Models for the Impact of Seasonal Weather Variation and Infections on Prey Predator Interactions in Serengeti Ecosystem

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Open Journal of Ecology 2022年第11期12卷 718-732页

作者： Raymond Charles oluwole daniel makinde Monica Kung’aro Department of Mathematics University of Dodoma Dodoma Tanzania Faculty of Military Science Stellenbosch University Cape Town South Africa

Interaction between prey and predator species is a complex and non-linear process. Understanding various phenomena in the dynamics of prey-predator systems is vital to both mathematical ecology and conservation biology. Mathematical models on prey-predator systems have been the hot sport providing important information regarding the interactions of prey and predator species in various ecosystems. In this paper, a review of the available mathematical models on prey-predator systems was done. Our aim was to assess their structure, behaviour, available control strategies, population involved and their ability in predicting the future behaviour of the ecosystems. We observed diversities in the reviewed mathematical models, some model incorporated factors such as drought, harvesting and prey refuge as the factors that affect ecosystems, some ignored the contribution of environmental variations while others considered the variable carrying capacity. Most of the models reviewed have not considered the contribution of diseases and seasonal weather variation in the dynamics of prey predator systems. Some of the reviewed models do not match the real situation in most modelled ecosystems. Thus, to avoid unreliable results, this review reveals the need to incorporate seasonal weather variations and diseases in the dynamics of prey predator systems of Serengeti ecosystem.

关键词： Prey Predator Weather Variation Disease Serengeti Ecosystem

Computational Modelling of Cholera Bacteriophage with Treatment

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Open Journal of Epidemiology 2015年第3期5卷 172-186页

作者： daniel S. Mgonja Estomih S. Massawe oluwole daniel makinde Mathematics Department University of Dar es Salaam Dar es Salaam Tanzania Faculty of Military Science Stellenbosch University Stellenbosch South Africa

This paper examines the computational modelling of cholera bacteriophage with treatment. A nonlinear mathematical model for cholera bacteriophage and treatment is formulated and analysed. The effective reproduction number of the nonlinear model system is calculated by next generation operator method. By using the next generation matrix approach, the disease-free equilibrium is found to be locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium point is not stable due to existence of forward bifurcation at threshold parameter equal to unity. Stability analysis and numerical simulations suggest that the combination of bacteriophage and treatment may contribute to lessening the severity of cholera epidemics by reducing the number of Vibrio cholerae in the environment. Hence with the presence of bacteriophage virus and treatment, cholera is self-limiting in nature.

关键词： Cholera Bacteriophage Treatment Vibrio cholerae Equilibrium Stability Effective Reproduction Number

Modelling the Optimal Control of Transmission Dynamics of <i>Mycobacterium ulceran</i>Infection

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Open Journal of Epidemiology 2015年第4期5卷 229-243页

作者： Magreth Anga Kimaro Estomih S. Massawe daniel oluwole makinde Mathematics Department University of Dar es Salaam Dar es Salaam Tanzania Faculty of Military Science Stellenbosch University Stellenbosch South Africa

This paper examines optimal control of transmission dynamics of Mycobacterium ulceran (MU) infection. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations, optimal control and computer simulation. The basic reproduction number of the reduced model system is obtained by using the next generation operator method. It is found that by using Ruth Hurwitz criteria, the disease free equilibrium point is locally asymptotically stable and using centre manifold theory, the model shows the transcritical (forward) bifurcation. Optimal control is applied to the model seeking to minimize the transmission dynamics of MU infection on human and water-bugs. Pontryagin’s maximum principle is used to characterize the optimal levels of the controls. The results of optimality are solved numerically using MATLAB software and the results show that optimal combination of two controls (environmental and health education for prevention) and (water and environmental purification) minimizes the MU infection in the population.

关键词： MU Optimal Control Stability Pontryagin’s Maximum Principle Reproduction Number

Mathematical Analysis of Control Strategies of HCV in a Community with Inflow of Infected Immigrants

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Advances in Infectious Diseases 2015年第1期5卷 1-13页

作者： Neterindwa Ainea Estomih S. Massawe oluwole daniel makinde Lucy Namkinga Mathematics Department University of Dar es Salaam Dar es Salaam Tanzania Faculty of Military Science Stellenbosch University Cape Town South Africa Department of Molecular Biology and Biotechnology University of Dar es Salaam Dar es Salaam Tanzania

In this paper, we derive and analyse rigorously a mathematical model of control strategies (screening, education, health care and immunization) of HCV in a community with inflow of infected immigrants. Both qualitative and quantitative analysis of the model is performed with respect to stability of the disease free and endemic equilibria. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Using Lyapunov method, endemic equilibrium is globally stable under certain conditions. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the HCV model in a community with inflow of infected immigrants. However, analysis shows that screening, education, health care and immunization have the effect of reducing the transmission of the disease in the community.

关键词： HCV Disease Infected Immigrants Stability Sensitivity Index Lyapunov Method Screening Education Health Care and Immunization

具有绝热自由表面的三阶流体在重力作用下沿斜面薄膜流动时的热临界

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应用数学和力学 2009年第3期30卷 353-359页

作者： O·D·玛金德黄锋(译) 张禄坤(校) 开普半岛理工大学工程系贝尔维尔7535南非不详

研究三阶流体在重力作用下,沿着一个倾斜等温的,带绝热自由表面时薄膜流动的热临界机理.假设是Arrhenius动力学意义下的发热反应,同时不计物质消耗.得到了动量和能量守恒的非线性控制方程,并以MAPLE为工具,基于一种特殊形式的Hermite-Pa... 详细信息

研究三阶流体在重力作用下,沿着一个倾斜等温的,带绝热自由表面时薄膜流动的热临界机理.假设是Arrhenius动力学意义下的发热反应,同时不计物质消耗.得到了动量和能量守恒的非线性控制方程,并以MAPLE为工具,基于一种特殊形式的Hermite-Padé近似技术,使用一种全新的数值逼近方法解之.这种半数值方法比之传统的方法,如有限差分法、频谱法、打靶法等,具有一定的优势.得到了解函数的解析结构,并对全部流动结构的重要性能,包括速度场、温度场、热临界和分岔加以讨论.

关键词：倾斜的等温面三阶流体 Hermite-Pade近似热临界

Effects of Navier slip on unsteady flow of a reactive variable viscosity non-Newtonian fluid through a porous saturated medium with asymmetric convective boundary conditions

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Journal of Hydrodynamics 2015年第6期27卷 934-944页

作者： RUNDORA Lazarus makinde oluwole daniel Department of Mathematics and Applied Mathematics University of LimpopoTurfloop Campus Faculty of Military Science Stellenbosch University

A study on the effects of Navier slip, in conjunction with other flow parameters, on unsteady flow of reactive variable viscosity third-grade fluid through a porous saturated medium with asymmetric convective boundary conditions is presented. The channel walls are assumed to be subjected to asymmetric convective heat exchange with the ambient, and exothermic chemical reactions take place within the flow system. The heat exchange with the ambient obeys Newton＇s law of cooling. The coupled equations, arising from the law of conservation of momentum and the first law of thermodynamics, then the derived system are non- dimensionalised and solved using a semi-implicit finite difference scheme. The lower wall slip parameter is observed to increase the fluid velocity profiles, whereas the upper wall slip parameter retards them because of backflow at the upper channel wall. Heat pro- duction in the fluid is seen to increase with the slip parameters. The wall shear stress increases with the slip parameters while the wall heat transfer rate is largely unaltered by the lower wall slip parameter but marginally increased by the upper wall slip parameter.

关键词： Navier slip saturated porous medium third-grade fluid temperature dependent viscosity convective boundary condi-tions

Potentials of NPK and Organic Fertilizers on Growth Performance of Cashew （Anacardium occidentale L,） Seedlings on Degraded Typic Alfisol Soils in Ibadan, Nigeria

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Journal of Agricultural Science and Technology(A) 2011年第6期1卷 876-881页

作者： R. R. Ipinmoroti O. S. O. Akanbi M. A. daniel L. A. Adebowale G. A. Adewoye E. A. makinde C. O. Kayode Soils and Plant Ntrition Division Cocoa Research Institute of Nigeris PMB 5244 Ibadan 20001 Oyo State Nigeria Department of Botany Lagos State University Ojoo 203115 Lagos State Nigeria Department of Soil Science Institute of Agriculture and Training Ibadan 20004 Oyo State Nigeria

Sequel to complaints by cashew farmers on poor establishment rate of cashew seedlings on rehabilitated moribund cashew plantations in south western Nigeria, a fertilizer trial involving the use of organic materials （cow-dung, poultry droppings, cocoa and kola pod husks） compared to NPK and control （no fertilizer） treatments was conducted on the growth performance of cashew seedlings at Ibadan, Nigeria. The fertilizers were applied to supply 15 g N seedlingl in 3 replications. Cashew seedling growth parameters and dry matter yield were determined. Fertilizers resulted to consistently general higher plant height, girth, number of leaves and leaf area compared to NPK and control. The differences in the mean values were however not significantly different for girth but it was significant （P 〈 0.5） for plant height, number of leaves and leaf area, while there was no particular regular trend for plant number of branches. Plant root lengths were significantly higher using the organic fertilizers than NPK and control. Similar trend was obtained in the dry weight values for plant leaf, stem, root and total dry matter yield. There was however no consistent significant effect on NPK usage over control for all the parameters. It was therefore deduced that optimal growth performance and better establishment of cashew seedlings could be obtained with the use of organic fertilizers rather than inorganic fertilizer. The use of cocoa pod husk followed by cow-dung and poultry droppings were outstanding in better growth and dry matter yield performance of cashew seedlings and were advised for this purpose.

关键词： Cashew (Anacardium occideltale) dry matter yield growth parameters organic fertilizer NPK.