iosr-Jm   Volume-16 ~ Issue-6 ~ Nov. – Dec. 2020

Abstract: In this paper we formulate a mathematical model based on the dynamics of Diabetes Mellitus and HIV(AIDS). The co-infection model has a locally asymptotically stable disease-free equilibrium (DFE) whenever, the basic reproduction number (ℛ0) that is a certain epidemiological threshold, is less than unity. It is also shown, using a Lyapunov function and Lasalle Invariance Principle, that the DFE of the co-infection model is globally –asymptotically stable (GAS) whenever ℛ0<1. If ℛ0>1 then the model has locally-asymptotically stable endemic equilibrium point (EEP). Numerical simulation suggest that the reduction of the effective contact rate of HIV and increase in the treatment rate can reduce the disease burden of co-infection..

Keywords: Equilibrium, Local and Global stability, Endemic Equilibrium..

[1]. Weiss R A (May 1993). 'How does HIV cause AIDS?'. Science. 260(5112):1273-9.
Bibcode:1993Sci…260.1273W.doi:10.1126/science. 8493571. PMID 8493571.
[2]. Diabetes Fact sheet N0312. WHO. October 2013. Archived from the original on 26 August 2013. Retrieved 25 March 2014.
[3]. Chandra (2009). Transmission Dynamics of a two sex Model for Herpes Simplex Virus Type-2. Canadian Applied Mathematics
Quarterly , Vol-17, Number-2.
[4]. Belfour Henry H.. Herpes group viruses and HIV infection. The PRN note Book.
[5]. Anderson and May (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University, London/NewYork, 1991..

Abstract: Parkinson's disease is a progressive neurodegenerative disorder, where new cells in the brain die slowly over time due to the loss of the substantia nigra causing the lack of dopamine. In order to tackle the accurate diagnosis of Parkinson disease issue, this research proposes to design of a new algorithm to efficiently discern Parkinson's disease patients from the healthy individuals using the binary particle swarm optimization method. The case-control study was designed to evaluate this algorithm by analyzing the electroencephalogram dataset of over 196 patients with Parkinson's disease and compare it with that of healthy controls of the same age and gender. The comparison includes other traditional deep learning, logistic regression and binary particle swarm optimization techniques to find out the most accurate one between the three methods..

[1]. P. Nirale, A. Paul, and K. S. Yadav, "Nanoemulsions for targeting the neurodegenerative diseases: Alzheimer's, Parkinson's and Prion's," Life Sci., vol. 245, p. 117394, 2020.
[2]. S. Choi, W. J. Jahng, S. M. Park, and D. Jee, "Association of age-related macular degeneration on Alzheimer or Parkinson disease: a retrospective cohort study," Am. J. Ophthalmol., vol. 210, pp. 41–47, 2020.
[3]. R. Matej, A. Tesar, and R. Rusina, "Alzheimer's disease and other neurodegenerative dementias in comorbidity: A clinical and neuropathological overview," Clin. Biochem., vol. 73, pp. 26–31, 2019.
[4]. R. Buettner, T. Rieg, and J. Frick, "Machine Learning based Diagnosis of Diseases Using the Unfolded EEG Spectra: Towards an Intelligent Software Sensor," in Information Systems and Neuroscience, Springer, 2020, pp. 165–172.
[5]. A. A. Bhurane, S. Dhok, M. Sharma, R. Yuvaraj, M. Murugappan, and U. R. Acharya, "Diagnosis of Parkinson's disease from electroencephalography signals using linear and self‐similarity features," Expert Syst., p. e12472, 2019.

Abstract: The spread crisis of opioid drugs has brought serious influence to American society. How to effectively control the spread of opioid drugs has become the focus of attention of government. Fortunately, differential equation propagation model provides us new ideas to deal with it. First, by analyzing the data in " NFLIS_data", we find that the spread trend of opioid drugs in different states is different with time. From a spatial point of view, opioid users are mostly distributed in the border areas of various states and have certain spread effects on the surrounding counties. Next, according to the drug spread mechanism, a differential equation model ( Model 1 ) is established. Using this model, combined with data analysis, the possible spread sources of fentanyl in five continents are screened. Two counties, PHILADELPHIA and HAMILTON, are selected to predict the time when heroin spread reaches the threshold state. We find that the spread of heroin in HAMILTON county shows a......

Keywords: Data analysis; Drug Spread System; Differential equation model

[1]. Federal Efforts to Combat the Opioid Crisis: A Status Update on CARA and Other Initiatives[EB/OL].[2017-12-12].https://www.drugabuse.gov/about-nida/legislative-activities/testimony-to-congress/2017/federal-efforts-to-combat-opioid-crisis-status-update-cara-otherinitiatives.
[2]. Federal Efforts to Combat the Opioid Crisis: A Status Update on CARA and Other Initiatives[EB/OL].[2017-12-12].https://www.drugabuse.gov/about-nida/legislative-activities/testimony-to-congress/2017/federal-efforts-to-combat-opioid-crisis-status-update-cara-otherinitiatives.
[3]. Daoyuan Fang, Mingjun wei. Mathematical modeling - method guidance and case analysis [M]. Zhejiang university press, 2011. 182-183Author．
[4]. Xiaoxiao Li, Yanping Deng. Risk and evaluation of opioids addiction in chronic pain control [J]. Chinese Journal of Drug Abuse Control, 2013, 19 (05): 271-274.
[5]. Chengliang Qian. Research on the Optimizing Strategy of Government Regulation of Public Service Advertising [D]. Nanchang University, 2018.

Abstract: The study used simulated datato investigate the performance of parametric survival models of Weibull, lognormal and logistic distributions in estimating the parameters with different random censoring percentages.Data of 300 observations were used for each of the distributionswith different censoring proportions, of 5%, 10%, 20%, 25%, and 50%. The parameters were evaluated and compared with the postulated parameters used in data generation. All three distributions performed well, where Weibull distribution slightly underestimated theparameters at 50% censored of both scale and shape parameter, showed a better estimate of the parameters at 25%, 20%, 10% and 5% censored. Lognormal distribution overestimated at all the five censoring percentages.......

Keywords: Weibull, Lognormal,Logistic, Likelihood, Random censoring and Survival analysis

[1]. Nielsen, R. O., Bertelsen, M. L., Ramskov, D., Møller, M., Hulme, A., Theisen, D., Finch, C. F., Fortington, L. V., Mansournia, M. A., &Parner, E. T. (2019). Time-to-event analysis for sports injury research part 2: time-varying outcomes. British journal of sports medicine,53(1), 70–78. https://doi.org/10.1136/bjsports-2018-100000
[2]. Fleming, Thomas R., and David P. Harrington.(1991). Counting Processes and Survival Analysis. New York: Wiley, 1991. Print. ISBN: 047152218x / 9780471522188 Quantity available:
[3]. Shelby Marie Cummings (2013). The Use of Survival Analysis Techniques AmongHighly Censored Data Sets.
[4]. Kalbfleisch, John,Prentice, Ross (2002). The statistical analysis of failure time data. 2nd ed; Journal of the American Statistical Association, 77 - 10.2307/1268689.
[5]. Prinja, S., Gupta, N., &Verma, R. (2010). Censoring in clinical trials: review of survival analysis techniques. Indian journal of community medicine : official publication of Indian Association of Preventive & Social Medicine, 35(2), 217–221. https://doi.org/10.4103/0970-0218.66859

Abstract: In modern finance, derivatives like options are actively traded on many exchanges throughout the world. Since pricing option is a challenging task, it attracts the attention of many researchers nowadays. In many cases calculation of large number of prices is required in short time, so fast and accurate calculation of option price is crucial. This paper introduces some fundamental concepts on underlying option valuation theory including implementation of computational tools. To do this, numerical methods such as Binomial Trees, Monte Carlo Simulation are discussed. Both these numerical techniques are used to price the most desirable European options. Hence the results are compared with the standard Black-Scholes-Merton Model with the help of a computer algebra system MATLAB.

Keywords: European options, Black-Scholes model, Binomial Tree, Monte Carlo Simulation.

[1]. Jeanette Schwarz Young, The Options Doctor: Option Strategies for every kind of Market, John Wiley & Sons, Inc. (2007).
[2]. Richard D. Irwin, Options Essential Concepts and Trading Strategies, 2nd Ed, Irwin Professional Publishing Inc. (1995).
[3]. John C. Hull, Options, Futures, and Other Derivatives, Global edition, 9th Ed, Pearson Education Limited (2015).
[4]. Nicolas Privault, Stochastic Finance: An Introduction with Market Examples, CRC Financial Mathematics Series (2014).
[5]. John C. Cox, Stephen A. Ross, Mark Rubinstein, Option Pricing: A Simplified Approach, Journal of Financial Economics, 7
(October 1979): 229-64.

Abstract: Have you ever experienced those annoying moments when you have to wait in line to get a service, unfortunately, this case continues to increase in urban societies. Pregnant women also encounter this unforeseen dilemma every time they go to participate in their antenatal visits. Health providers should have the abilities to deliver safe, efficient and smooth services to their customers. This project worked to optimizing this occurrence to produce effective service rate and reduce the waiting time for this expectant mothers at a specific hospital with the aid of a systematic model called queuing model. The result generated from this model was used to analyze the performance measures of the queue formed in Dalhatu Araf Specialist Hospital Lafia.

Keyword: Antenatal, queuing theory, waiting time, service time, servers.

[1]. Bailey, N.T.J. A study of queues and appointment systems in hospital out-patient
departments, with special reference to waiting times, Journal of the Royal Statistical Society, 1952, 14, 2, :185{199.
[2]. Cochran, J. K. and Roche, K. T. A multi-class queuing network analysis methodology for improving hospital emergency
department performance, Computers & Operations Research,2009, 36, 1497{1512.
[3]. Green, L. Queueing analysis in healthcare, in Patient Flow: Reducing Delay in Healthcare Delivery, Hall, R.W., ed., Springer, New
York, 2006,281-308.
[4]. Kembe, M. M., Onah, E. S., &Iorkegh, S. A Study of Waiting and Service Costs of a Multi Server Queuing Model in a Specialist
Hospital. Ijacst,2012, 1(8), 19{23
[5]. Kembe, M.M.&Onoja,A.A. The Application of Queuing Theory on Patient Waiting Time in Ante-natal Care Clinic, International
Journal of Science and Technology, 2018, Vol.6,Issue 1, pg 15-22

Abstract: In this paper, we study some qualitative properties of the solutions for the following difference equation.....

Keywords: boundedness, local stability, periodicity, global stability. MathematicsSubjectClassification:39A10

[1]. C. Cinar, On the positive solutions of the difference equation Appl. Math. Comp.150 (2004) 21-24.
[2]. J.H. Conway, H.S.M. Coxeter, Triangulated polygons and frieze patterns, Math.Gaz. 57 (400) (1973) 87-94.
[3]. Eduardo Liz, On explicit conditions for the asymptotic stability of linear higher order difference equations, J. Math. Anal. Appl. 303 (2) (2005) 492 498.
[4]. E.M. Elabbasy, H. El-Metwally, E.M. Elsayed, Global attractivity and periodiccharacter of a fractional difference equation of order three, Yokohama Math. J.53 (2007) 91-102.
[5]. H. El-Metwally, "Qualitative Proprieties of some Higher Order Difference Equations", Computers and Mathematics with Applications. Vol.58, No.4, (2009)686-692.

Abstract: Our aim in this paper is to investigate the boundedness, global attractively, locally asymptotically stability of the positive solution of the difference equations of form

Keywords: Boundedness, periodicity, global stability, difference equations

[1]. A. Amleh, E. Grove, G. Ladas and D. Georgiou, "On the Recursive Sequence....