Open Access Original Research Article

An Algorithm for Solutions of Hammerstein Integral Equations with Maximal Monotone Operators in Classical Banach Spaces

M. O. Uba, M. A. Onyido

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/BJMCS/2016/28512

Let = lp , 2  p < ∞. Let F : X → X* and X* → X be bounded maximal monotone mappings such that the Hammerstein equation u+KFu = 0 has a solution. An explicit iteration sequence is constructed and proved to converge strongly to a solution of this equation. Our method of proof is also of independent interest.

Open Access Original Research Article

Analysis of Dynamics of HIV-1 Associated Kaposi Sarcoma during HAART and ACI

Frank Nani, Mingxian Jin

Journal of Advances in Mathematics and Computer Science, Page 1-22
DOI: 10.9734/BJMCS/2016/20358

Aims: To formulate, analyze, and perform investigative computer simulations for clinically plausible mathematical model depicting the patho-physiodynamics of HIV-1 associated Kaposi Sarcoma (KS) during Highly Active Anti-Retroviral Therapy (HAART) of AIDS and Adoptive Cellular Immunotherapy (ACI). The basic principle of digital combination therapy involving HAART and ACI is exhibited in the computer simulations.

Study Design: The mathematical model proposed in the current research is based on the results of the state-of-the-art data published in peer-reviewed journals relating to HAART, KS, and ACI. Using Dynamic Systems Theory, the clinical data is reformulated into a system of non-linear deterministic differential equations involving six model variables: non-HIV-1 infected CD4+ T lymphocytes, HIV-1 infected lymphocytes, free HIV-1 virions in the blood plasma, HIV-1 specific cytotoxic CD8+ T lymphocytes/ex-vivointerleukin-2 (IL-2) incubated CD8+ T cells, HAART drug molecules, and the KS cancer cells. The model incorporates all appropriate stoichiometric interaction rate coefficients, apoptotic rate constants, rate constants for viral recruitment from latent reservoirs, and other relevant parameters. The role of CD4+ T cell-induced syncytia in modulating the outcome of HAART and ACI is exhibited in the computer simulations using clinically plausible hypothetic patient physiological parametric configurations.

Place and Duration of Study: This research was conducted at Fayetteville State University (FSU), Fayetteville, North Carolina, USA.  The digital version of the model was initiated in the summer of 2015 under the HBCU Graduate STEM Summer Grant in 2015.

Methodology: The equilibrium points, also known as the physiological outcomes were computed and the local stability at these points were analyzed utilizing the Hartman-Grobman theory, the principles of linearized stability, Banach space techniques, and Lozinskii matrix based stability. The clinically desirable physiological outcomes are further analyzed to obtain plausible robust criteria under which the HIV-1 virions, HIV-1 infected CD4+ lymphocytes and KS cells are annihilated. In particular, some scenarios of therapeutic failure are also discussed.

Results: Theoretical digital criteria for remission and possible cure of KS and AIDS are derived in terms of biophysically measurable parameters. The model simulations incorporate scenarios with and without HIV-1 induced syncytia. The digital prognosis of KS and the associated HIV-1 AIDS are exhibited in terms of biophysically measurable mathematical criteria. In particular, the computer simulations use hypothetical patient parametric configurations to elucidate the quantitative dynamics of KS and associated HIV-1 AIDS during HAART and ACI.

Conclusion: This research has demonstrated that under certain patient parametric configurations, a higher density of syncytia prevents reconstitution of CD4+ T cells at various doses of HAART drug cocktail.  It also establishes theoretically it is possible for HAART to annihilate HIV-1 infected CD4+ T cells and HIV-1 virions without necessarily eliminating KS.

Open Access Original Research Article

Online Elman Neural Network Training by Genetic Algorithm

Ali Hussein Hasan, Watheq Hayawi Laith

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2016/29060

Although most offline and online training algorithms based on gradient search techniques like backpropagation algorithm and its modifications or on Kalman filter approaches, it has been shown that these techniques are severely limited in their ability to find global solutions, they converge slowly, get local minimization too easily and courses oscillation. Global search techniques have been identified as a potential solution to this problem, but they are limited to offline training because of the long time of convergence. The paper is focused on presenting of applying online genetic algorithm to train recurrent artificial neural networks. Here; improvement are made on the real coding genetic algorithm by introducing a reserve elite chromosome. The new approach is tested on the Elman network (which generally suffer from very long training time) for several types of dynamic system plants. The simulation results show that the proposed algorithm is able to train ENN with less training data set in corresponding to Kalman filter training algorithm.

Open Access Original Research Article

Optimal Control of Ebola Transmission Dynamics with Interventions

F. T. Oduro, George Apaaboah, Joseph Baafi

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/BJMCS/2016/29372

In this paper, SEIR epidemic model is used to study Ebola transmission dynamics and compared with SIR model against World Health Organisation data from Sierra Leone. It was found that the constructed SEIR model was more representative of the situation in Sierra Leone. In addition, the impact of quarantine, vaccination and/ or both interventions on the transmission dynamics of the disease was studied. The introduction of interventions caused the disease free equilibrium to become stable. Finally, the optimal control problem was solved for the transmission dynamics of the disease using these interventions as control variables. It was observed that the best intervention strategy is to implement require a combination of both quarantine and vaccination.

Open Access Original Research Article

A Theorem for Zeros of Maximal Monotone and Bounded Maps in Certain Banach Spaces

M. A. Onyido, M. O. Uba, M. I. Uzochukwu, P. U. Nwokoro, E. E. Otubo

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/28720

Let be a p-uniformly convex and q-uniformly smooth real Banach space with dual space X*. Let T1 : X → 2Xand T2 : X → 2X* be bounded maximal monotone mappings. An iterative process is constructed and proved to converge strongly to a zero of sum of the two maps.

Open Access Original Research Article

Utility Analysis of an Emergency Medical Service Model Using Queuing Theory

T. K. Rotich

Journal of Advances in Mathematics and Computer Science, Page 1-18
DOI: 10.9734/BJMCS/2016/29369

Aims/ Objectives: To use queuing model to deter mine the optimum waiting and service cost in a hospital ICU emergency service.

Study Design: Modeling and Simulation.

Place and Duration of Study: ICU Emergency Service Department, Moi Teaching and Referral Hospital (MTRH), Uasin Gishu - County, between June 2016 and July 2016.

Methodology: Use of M/M/s queuing model to analyze ICU services using secondary data of MTRH emergency patients arrival and service rates together with estimated service cost of available 6 beds. Waiting cost estimated using formulated Modified Normal Loss function.

Results: With an average individual tolerance of τ=0.083 hrs and average response time of =0.083 hrs, the present scenario of 6 ICU beds in MTRH is operating at a service cost of Ksh 60 and patient queuing cost of Ksh 415.53 per hour. The length of the queue is 1.4 hr or approximately 34 patients per day. The optimum number of beds required for the facility to operate with zero response time and zero quality tolerance is 18 beds. This will facilitate the reduction of queuing cost to 153.98 and total cost to 333.98.

Conclusion: The current status of ICU emergency services at MTRH is costly to both the health facility and the patients. Individuals seeking such services may either opt to get similar services elsewhere at an opportunity cost of Ksh 641.39 per hour of delay. With 1.4 patients waiting in the queue every hour, this accumulates to 34 patients per day. Increasing ICU beds to 18 minimizes the length of the queue to 6 patients per day and queuing cost by 76% and reduces the total cost by 65%. This will reduce the financial burden of the patients and increase the chances of saving lives during emergency cases. These predictors, however, need further work and inclusion of related services to give a bigger and better picture of the facility.

Open Access Original Research Article

Solving Time Fractional Sharma-Tasso-Olever Equation using Fractional Complex Transform with Iterative Method

Bhausaheb R. Sontakke, Amjad Shaikh

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2016/29039

In this paper, we consider time fractional Sharma-Tasso-Olever equation based on Jumarie's modified Riemann-Liouville derivatives. By using fractional complex transform the time fractional Sharma-Tasso-Olever equation reduces to nonlinear partial differential equation and then new iterative method is applied to get approximate solutions. The Numerical results and the graphs of the solutions are compared with the exact solutions to verify the applicability, efficiency and accuracy of the method.