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• Open Access   Article

  A Mathematical Model for the Transmission of Measles with Passive Immunity

  E.M. Musyoki, R.M. Ndung’u, S. Osman

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.1-8, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.18

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  Abstract
  A mathematical model of the transmission dynamics of measles incorporating passively immune class is developed. The dynamics of the disease are expressed with the help of a set of ordinary differential equations. The model is analysed qualitatively and quantitatively. Equilibrium points of the determined and their stability analysed. From the study it has been shown that for a stable disease-free equilibrium the reproduction number is less than 1 and more than 1 for an unstable disease-free equilibrium. The spread of the disease in the population is dependent on the level of between the susceptible individuals and the infected individuals. The rate at which passive immunity in an infant is lost also has a great impact on the spread of the disease.

  Key-Words / Index Term
  Equilibrium points, disease free equilibrium, measles, basic reproduction number, stability

  References
  [1] A. Dabbagh, R.L. Laws, C. Steulet, et.al, “Progress Toward Regional Measles Elimination – Worldwide, 2000-2017”, MMWR, Vol. 67, No. 47, pp. 1323-1329, 2018.
  [2] M.O Fred, J.K. Sigey, J.A. Okello, M. James, J. Okwoyo & Giterere, Kang’ethe. “Mathematical Modeling on the Control of Measles by Vaccination. Case Study of KISII County, Kenya”, The SIJ Transactions on Computer Science Engineering & its Applications (CSEA), Vol. 2, issue 3, pp. 61-69, 2014.
  [3] J.D. Murray, “Mathematical Biology”, Vol. I, Interdisciplinary Applied, 2003.
  [4] K. Manakongtreecheep, R. Davis, “A Review of measles control in Kenya, with focus on recent innovations”, The Pan African Medical Journal, Vol. 27, Supp 2, pp. 15, 2017.
  [5] M. Kasidet, D. Robert, “A review of measles control in Kenya, with focus on recent innovations”,Pan African Medical Journal, Vol. 27,Supp 3, pp. 15, 2017.
  [6] A.M. Pertet, D. Kaseje et. al., “Under vaccination of children among Maasai nomadic pastrolists in Kenya: is the issue geographic mobility, social demographics or missed opportunities”, BMC Public Health, Vol. 18, pp. 1389, 2018.
  [7] O.O. Malande, D. Munube, R.N. Afaayo et. al. “Barriers to effective uptake and provision of immunization in a rural district in Uganda”, PLOS one, Vol. 14, No. 2, pp. e0212270, 2019.
  [8] O. Diekmann, P. Heesterbeek, J. Metz, “On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations”, J. Math. Biol., Vol. 28, pp. 365-382, 1990.
  [9] R.M. Ndung’u, G.P. Pokhariyal, R.O. Simwa. “Modelling the effect of periodic temperature on malaria transmission dynamics”, AJOMCOR, Vol. 13, No. 2, pp. 91-105, 2016.
  [10] S.W. Indrayani, N. Binatari, “Stability Analysis of SEIR Model (Susceptible-Exposed- Infected-Recovered) with Vaccination on the Spread of Measles in Sleman Yogyakarta”, Yogyakarta State University, 2015.
  [11] S. Edward, R.E. Kitengeso, G.T. Kiria, N. Felician, G.G. Mwema, A.P. Mafarasa, “A Mathematical model for control and elimination of the transmission dynamics of measles”, Journal of Applied and Computational Mathematics, Vol. 4, No. 6, pp. 396-408, 2015.
  [12] E. Leuridan, N. Hens et al, “Early waning of maternal measles antibodies in era of measles elimination; longitudinal study”, BMJ, Vol. 340, c 1626, 2010.
  

  Citation
  E.M. Musyoki, R.M. Ndung’u, S. Osman, "A Mathematical Model for the Transmission of Measles with Passive Immunity," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.1-8, 2019

• Open Access   Article

  Strong Regularity in Near-Rings

  S Narmada, Sidhartha Sarma S K

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.9-10, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.910

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  Abstract
  The aim of this paper is to prove some concepts related with strong regularity and strong reducedness in near-rings. We arrive a conclusion that all reduced and regular near-rings are strongly regular and strongly reduced near-rings. Also we discuss the idea of semicentral in near-rings

  Key-Words / Index Term
  Near-rings, Regular, Reduced, Strongly regular, Strongly reduced, Right semicentral

  References
  [1] G Mason, “Strongly regular near-rings”, Proc.EdinburghMath. Soc.23 (1983), 27-35.
  [2] Y V Reddy and C V L N Murty, “On strongly regular Near- rings”, Proc. Edinburgh Math. Soc.27(1984),61-64.
  [3] Yong Uk Cho and Yasuyuki Hirano, “Strong reducedness and strong regularity for near-rings”, Kyangpook Math.J 43(2003), 587-592.
  [4] S Narmada and S Anil Kumar, “Characterizations of strongly regular near-rings”, FJMS, 48 (2),(2011),211-216.
  [5] G Pilz, “Near-rings”, North-Holand publishing company, Amsterdam, NewYork, Oxford (1983).
  [6] S Narmada and Sidhartha Sarma S K, “Homomorphism Strong Regularity Strong Reducedness and related Concepts”, International Journal of Mathematical Archive-9(4),2018,78-82.
  [7] J R Clay, “The near-rings on groups of low order”, Math.Z.(1968),364-371.
  

  Citation
  S Narmada, Sidhartha Sarma S K, "Strong Regularity in Near-Rings," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.9-10, 2019

• Open Access   Article

  Totally g#ψ - Continuous Functions and g#ψ - Totally Continuous Functions in Topological Spaces

  S . Deepika, N. Balamani

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.11-15, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.1115

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  Abstract
  In this paper we introduce a new type of functions called totally g#ψ - continuous function and g#ψ - totally continuous functions in topological spaces. Also we study the interrelation between these functions.

  Key-Words / Index Term
  Totally continuous function, g#ψ - continuous function, g#ψ - closed set and g#ψ - open set

  References
  [1]. Balachandran, K., Sundaram , P. and Maki , H. , “on generalized continuous maps in topological spaces” , Mem. Fac. Sci .Kochi Univ. Math , vol .12, pp.5-13, 1991.
  [2]. Bhattacharyya, P. and Lahiri, B.K. “ Semi-generalized closed sets in topology”, Indian J. Math., vol .29, pp 376-382 , 1987.
  [3]. Jain, R.C. “ Role of regular open sets in general topology”, Ph.D. thesis, Meerut University, Meerut, India, 1980.
  [4]. Kanimozhi, K. and Balamani, N. “g#ψ - closed sets in topological spaces” Imperial Journal of Interdisciplinary Research (IJIR) - vol .3, pp.1931-1935, 2017.
  [5]. Kanimozhi, K. and Balamani, N. “g#ψ - closed sets in topological spaces, M.Sc Thesis” , Avinashilingam Institute for Home Science and Higher Education for Women University, Coimbatore , India. 2017.
  [6]. Levine, N. “ semi open sets and semi continuity in topological spaces”, Amer. Math. Monthly, vol.70, pp.36-41, 1963.
  [7]. Levine, N. “Generalized closed sets in topology”, Rend. Circ. Math. Palermo, vol.19, pp.89 - 96, 1970.
  [8]. Veera kumar, M.K.R.S. “ Between semi-closed sets and semi-pre closed sets”, Rend. Istit. Mat. Univ. Trieste, (ITALY), XXXXII, pp.25-41, 2000.
  

  Citation
  S . Deepika, N. Balamani, "Totally g#ψ - Continuous Functions and g#ψ - Totally Continuous Functions in Topological Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.11-15, 2019

• Open Access   Article

  A Lindley Distribution Model for Intravenous Administration of Ghrelin Stimulates GH Secretion in Vagotomized Patients and Normal Subjects

  M. Kaliraja, K. Perarasan

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.16-20, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.1620

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  Abstract
  A Lindley distribution is solitary approach to state the lifetime of a process or device. It can be employed in a broad range of meadows, together with engineering, medicine and biology. In this paper, we have utilized the two parameter lindley distribution to analyze the involvement of vagotomized nerve in gherlin-induced growth hormone (GH) secretion in humans. Further, the growth hormone responses to gherlin were compared in-between the vagotomized patients with gastrectomy and normal subjects with the help of lindley distribution.

  Key-Words / Index Term
  Lindley distribution, Growth hormone, Parameters, Mean residual life function

  References
  [1] D. V. Lindley, “Fiducial Distributions and Bayes. Journal of the Royal Statistical Society, Series B, Vol. 20, No. 1, 1958, pp. 102-107.
  [2] D. V. Lindley, “Introduction to Probability and statistics From Bayesian Viewpoint,” Cambridge University Press, New York, 1965.
  [3] E. G. Deniz and E. C. Ojeda, “The discreate lindley distribution-Properties and Applications,” Journal of Statistical Computation and Simulation, Vol. 81, No. 11, 2011, pp. 1405-1416.
  [4] M. Sankaran, “The Discrete Poisson-Lindley distribution,” Biometrics, Vol. 26, No. 1, 1970. pp. 145-149.
  [5] Sato M, Chihara K, Kita T, Kashio Y, Okimura Y, Kitajima N & Fujita T. Physiological role of somatostatin-mediated autofeedback regulation for growth hormone: importance of growth hormone in triggering somatostatin release during a trough period of pulsatile growth hormone release in conscious male rats. Neuroendocrinology 1989 50 139–151.
  [6] Kojima M, Hosoda H, Date Y, Nakazato M, Matsuo H & Kangawa K. Ghrelin is a growth-hormone-releasing acylated peptide from stomach. Nature 1999 402 656–660.
  [7] Howard AD, Feighner SD, Cully DF, Arena JP, Liberator PA, Rosenblum CI et al. A receptor in pituitary and hypothalamus that functions in growth hormone release. Science 1996 273 974–977.
  [8] Takaya K, Ariyasu H, Kanamoto N, Iwakura H, Yoshimoto A, Harada M et al. Ghrelin strongly stimulates growth hormone release in humans. Journal of Clinical Endocrinology and Metabolism 2000 85 4908–4911.
  [9] Rama Shanker, Shambhu Sharma, Ravi Shanker, A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data, Applied Mathematics, 2013, 4, 363-368
  [10] Ryoko Takeno, Yasuhiko Okimura, Genzo Iguchi, Masahiko Kishimoto, Takumi Kudo, Kentaro Takahashi, Yutaka Takahashi, Hidesuke Kaji, Masakazu Ohno, Hajime Ikuta, Yoshikazu Kuroda, Tetsuji Obara, Hiroshi Hosoda, Kenji Kangawa and Kazuo Chihara, Intravenous administration of ghrelin stimulates growth hormone secretion in vagotomized patients as well as normal subjects European Journal of Endocrinology (2004) 151 447–450, ISSN 0804-4643.
  

  Citation
  M. Kaliraja, K. Perarasan, "A Lindley Distribution Model for Intravenous Administration of Ghrelin Stimulates GH Secretion in Vagotomized Patients and Normal Subjects," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.16-20, 2019

• Open Access   Article

  Gallai-Type Theorems in Gallai Fuzzy Graphs on Domination Parameters

  M. Kaliraja, G. Karlmarx

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.21-25, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.2125

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  Abstract
  The Gallai fuzzy graph Γ(G) of a fuzzy graph G has the fuzzy edges of G as its fuzzy vertices and two distinct fuzzy edges of G are fuzzy incident in G, but do not span a fuzzy triangle in G. The Gallai fuzzy graphs are fuzzy spanning Gallai sub graphs of the well-known Class of fuzzy line graphs. Let γ(Γ(G)) and i(Γ(G)) denote the minimum fuzzy cardinality of a fuzzy dominating set of a Gallai fuzzy graph Γ(G)= (σ, μ) with n fuzzy vertices and maximum fuzzy degree Δ(Γ(G)), (Γ(G))≤ n-Δ(Γ(G), i(G) ≤ n-Δ(Γ(G)). In this manuscript, we characterized the fuzzy connected bipartite Gallai fuzzy graphs which achieve this upper bound. Here, we have shown that an arbitrary Gallai fuzzy Graph G are furnished with two conditions which are necessary if γ(Γ(G)) + Δ(Γ(G))= n and are sufficient to achieve n - 1 ≤ γ(Γ(G))+Δ(Γ(G)) ≤ n.

  Key-Words / Index Term
  Gallai fuzzy graph, Gallai-type theorems, fuzzy domination parameters

  References
  [1] L. A. Zadeh, Fuzzy Sets, Information and Control, vol.8, pp. 338-353, 1965.
  [2] A. Rosenfeld, Fuzzy Graphs in: Zadeh. L. A., Fu, K. S.,Shimura, M(Eds), Fuzzy sets and their application, Academic press, Newyork, 1975.
  [3] Van Bang Le, Gallai and anti Gallai Graphs, Discr. Maths, vol.159, pp179-189, 1996..
  [4] S. Aparna Lakshmanan, S. B. Rao, A. Vijayakumar, Gallai and anti-Graphs of a Graph, Mathematica Bohemica, Vol. 132, No. 1, pp. 43-54, 2007.
  [5] A. Somasundaram, S. Somasundaram, Domination in Fuzzy Graphs-1, Elsevier Science, 19, pp787-791, 1965.
  [6] A. Nagoorgani, P. Vadivel, A Study On Domination, Independence Domination and Irredundance in Fuzzy Graph, Applied Mathimatical Science, 5(47), pp.2317-2325, 2011.
  [7] Gayla. S. Domke, Jean. E. Dunbar, Lisa R. Markus, Gallai-type theorems and Domination parameters,167/168, pp.237-248, 1996.
  [8] E.J. Cockayne and S.T. Hedetniemi. Gallai theorems for graphs, Hypergraphs, and Set System, Discr.Maths.Vol.72, pp.35-47, 1988.
  [9] Berge, C., Theory of Graphs and its Applications, Methuen, London, 1962.
  [10] Ore, O., 1962, “Theory of graphs”, Amer. Math. Soc. Colloq. Publi., Amer. Math. Soc. Providence. RI, Vol. 381962
  

  Citation
  M. Kaliraja, G. Karlmarx, "Gallai-Type Theorems in Gallai Fuzzy Graphs on Domination Parameters," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.21-25, 2019

• Open Access   Article

  A Stochastic Model with Antigenic Diversity Threshold Time Using Erlang Truncated Exponential Distribution using Order Statistics

  R. Kannan, G. Parthasarathi

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.26-33, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.2633

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  Abstract
  This study is based on a stochastic model for predicting the seroconversion time of HIV infected using the inter-contact time between successive contacts forms an order statistics. The contribution to antigenic diversity due to sexual contacts on successive occasions is important factor in this paper it is assumed that the threshold following Erlang truncated exponential distribution and inter-arrival times which forms a smallest order statistics. The expected time to seroconversion and variance are derived and numerical illustration is also given using simulated data.

  Key-Words / Index Term
  Acquired Immune Deficiency Syndrome, Human Immunodeficiency Virus, Seroconversion, Antigenic diversity threshold, Smallest Order statistics

  References
  [1] Esary JD, Marshall AW, Proschan F. Shock models and Wear processes, Ann. Probability, 1973; 1(4):627-649.
  [2] Kannan R, Chandrasekar K. A stochastic model for the estimation of expected time to seroconversion of HIV infected using order statistics’. International Journal of World Research. 2015; 1(23):1-8.
  [3] Kannan R, Ganesan A, Sathiyamoorthi R, G. A Stochastic Model for the Estimation of Time to Seroconversion of HIV Infected using Order Statistics, Bio-Science Research Bulletin. 2008; 24(1):44-47.
  [4] Kannan R, Thirumurugan A, Sathiyamoorthi R, Malarvizhi G. A stochastic model with the antigenic diversity threshold of HIV transmission using order statistics’. Bio-Science Research Bulletin. 2010; 26(1):45-55.
  [5] Kannan R, Iyappan M (2017), A stochastic model with antigenic diversity threshold of HIV transmission using smallest order statistics, International Journal of recent scientific research. Vol (8) Page 19083-19087.
  [4] Kannan R, Kavitha S, Sathiyamoorthi R. A stochastic approach to determine the expected time to seroconversion of HIV infected using order statistics, Journal of the Indian Academy of Mathematics. 2013; 35:131-141.
  [6] Nowak MA, May RM. Mathematical Biology of HIV Infections: Antigenic Variation and Diversity Threshold’, Mathematical Biosciences. 1991; 106:1-21.
  [7] Ratchagar NP, Vijaya S, Sathiyamoorthi R, Kannan R. A stochastic model for estimation of expected time to seroconversion of HIV infected using order statistics, Proceedings of the National Conference on Mathematical and Computational Models, PSG College of Technology, Coimbatore, 2003, 37-42.
  [8] Stilianakis N, Schenzle D, Dietz K. On the Antigenic Diversity Threshold Model for AIDS, Mathematical Biosciences. 1994; 121:235-247.
  

  Citation
  R. Kannan, G. Parthasarathi, "A Stochastic Model with Antigenic Diversity Threshold Time Using Erlang Truncated Exponential Distribution using Order Statistics," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.26-33, 2019

• Open Access   Article

  Projection of Age-Specific Fertility Rates of India using MCMC technique in the Bayesian Inference

  Anurag Verma, Abhinav Singh, Gyan Prakash Singh, Pramendra Singh Pundir

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.34-42, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.3442

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  Abstract
  In this paper, is an attempt to expand the framework of the population projections developed in early studies (World Population Prospect (2012); Mahsin & Hossain (2012)). In Population projection, the two main component, first, the Total Fertility Rate and second, Life Expectancy at Birth. In early studies these components is projected in the future, then converted into Age-Specific Fertility Rate and Age-Specific Mortality Rate after that combine these two components into well-known Cohort-component methods to project population. This study is attempt to summarize the advantages and disadvantages of this approach. The main purpose of this study is design to project future level of fertility by age under Bayesian approach to measure uncertainty in the future. This approach is illustrating in the Indian context from 1971 to 2012 and is later used to project the ASFR levels in the future to 2061.

  Key-Words / Index Term
  Bayesian modelling; Markov chain Monte Carlo; Total Fertility Rates; World Population Prospects; Bayesian forecasting; non-linear regression model

  References
  [1] UNPD (2013). World population prospects: the 2012 revision. Population division of the department of economic and social affairs of the United Nations Secretariat, New York.
  [2] Mahsin, M., & Hossain, S. S. (2012). Population forecasts for Bangladesh, using a Bayesian methodology. Journal of health, population, and nutrition, 30(4), 456.
  [3] Alkema, L., Raftery, A. E., Gerland, P., Clark, S. J., Pelletier, F., Buettner, T., & Heilig, G. K. (2011). Probabilistic projections of the total fertility rate for all countries. Demography, 48(3), 815-839.
  [4] Gerland, P., Raftery, A. E., Ševčíková, H., Li, N., Gu, D., Spoorenberg, T., ... & Bay, G. (2014). World population stabilization unlikely this century. Science, 346(6206), 234-237.
  [5] Stover, J., & Kirmeyer, S. (2005). DemProj. Version 4. A computer program for making population projections.
  [6] International Institute for Population Sciences (IIPS) and Macro International. (2017). National Family Health Survey (NFHS-4), 2015–16: India.
  [7] Registrar General, I. (2018). Compendium of India’s fertility and mortality indicators 1971-2013 based on The Sample Registration System (SRS). New Delhi Registrar General: India.
  [8] Registrar General, I. (2015). Civil Registration System 2015. Office of the Registrar General, India, Ministry of Home Affairs, Vital Statistics Division, New Delhi: India.
  [9] Registrar General, I. (2006). Population Projections for India and States: 2001-2026. Report of the Technical Group on Population Projections constituted by the Planning Commission, New Delhi.
  [10] Spiegelhalter, D., Thomas, A., Best, N., & Gilks, W. (1996). BUGS 0.5: Bayesian inference using Gibbs sampling manual (version ii). MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK, 1-59.
  [11] Spiegelhalter, D., Thomas, A., Best, N., & Lunn, D. (2003). WinBUGS user manual.
  [12] Gelman, A., Stern, H. S., Carlin, J. B., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis. Chapman and Hall/CRC.
  [13] Kruschke, J. (2014). Doing Bayesian Data Analysis: A Tutorial With R, Jags, And Stan. Academic Press.
  [14] Spiegelhalter, D. J., Best, n. G., Carlin, B. P., & Van Der Linde, a. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(4), 583-639.
  

  Citation
  Anurag Verma, Abhinav Singh, Gyan Prakash Singh, Pramendra Singh Pundir, "Projection of Age-Specific Fertility Rates of India using MCMC technique in the Bayesian Inference," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.34-42, 2019

• Open Access   Article

  Mathematical Model of Malaria Fever in the Presence of Two Species of Mosquitoes

  P. Baghel, T.K. Jhala, V.H. Badshah

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.43-49, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.4349

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  Abstract
  In this study, we assume that both the human and mosquito populations are constant. A dynamical model of malaria fever is proposed and analyzed. The Routh-Hurwitz criteria are used to determine the stability of the model. The conditions which would lead to either the disease free equilibrium state or the endemic equilibrium state is determined. We use mathematical models to find the alternative that propose a model to govern the host of growth, development of change within the two species of malaria. By examine the given model, it has been found that the epidemics involve both species of malaria in the same area are possible.

  Key-Words / Index Term
  Mathematical Model, Malaria Fever, Basic Reproductive Number, Equilibrium Point, P. falci-parum

  References
  [1] https://www.who.int
  [2] Y. Xiao, Study of Malaria Transmission dynamics by Mathematical Models, Western University Scholarship @Western, 2011.
  [3] A. A. Gebremeskel, H. E. Krogstad, Mathematical Modeling of Endemic Malaria Transmission, American Journal of Applied Mathematics, 3(2), 36-46, 2015.
  [4] S. Naowarat, I. Ming Tang, Transmission Model of Chikungunya Fever in the Presence of Two Species of Aedes Mosquitoes, American Journal of Applied Sciences, 10(5), 449-459, 2013.
  

  Citation
  P. Baghel, T.K. Jhala, V.H. Badshah, "Mathematical Model of Malaria Fever in the Presence of Two Species of Mosquitoes," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.43-49, 2019

• Open Access   Article

  Stochastic Time Series Modeling for Rice Production in Andhra Pradesh

  S. C. Thasleema, Ahammad Basha Shaik

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.50-55, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.5055

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  Abstract
  Rice is the chief food grain of Indian population. Andhra Pradesh ranks fifth in the rice production in the country. Due to increase in demand of rice over the years, the modeling and forecasting of rice production over the years is very important. An Auto-Regressive Integrated Moving Average (ARIMA) methodology has been successful in describing and forecasting rice production in past studies. In the present study, ARIMA stochastic modeling is used for describing rice production in Andhra Pradesh. The yearly rice production data of Andhra Pradesh from 1980-81 to 2016-2017 has been used for validation of the model. The Statistical software SAS 9.3 is used for analyzing the data. The ARIMA (0, 1, 1) model is selected as the best model based on the minimum values of Root Mean Square Error (RMSE), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for the rice production of data in Andhra Pradesh. The forecasting of rice production was estimated from 2015-16 to 2026-27 using ARIMA approach.

  Key-Words / Index Term
  Rice production, ARIMA, Andhra Pradesh, SAS, Stochastic Time series

  References
  [1]. Reserve Bank of India (RBI). “Handbook of Statistics on Indian States 2017-18”. Reserve Bank of India, India, pp.196-198, 2018.
  [2]. Box, G.E.P., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. “Time Series Analysis: Forecasting and control”. 5th Edition, John Wiley & Sons, Inc., USA, 2016.
  [3]. Rahman, N. M. F. “Forecasting of boro rice production in Bangladesh: An ARIMA approach”, Journal of Bangladesh Agricultural University, Vol. 8, Issue 1, pp.103-112, 2010.
  [4]. Awal, M. A., and Siddique, M. A. B. “Rice production in Bangladesh employing by ARIMA model”, Bangladesh Journal of Agricultural Research, Vol. 36, Issue 1, pp. 51-62, 2011
  [5]. Badmus, M. A. and Ariyo, O. S. “Forecasting cultivated area and production of Maize in Nigerian using ARIMA Model”, Asian Journal of Agricultural Sciences, Vol. 3, issue 3, pp. 171-176, 2011.
  [6]. Zakari, Seydou and Ying, Liu. “Forecasting of Niger production and harvested area”, Asian Journal of Agricultural Sciences, Vol. 4, Issue 4, pp.308-313, 2012.
  [7]. Venkatramana Reddy, S., Karthick Kumar Reddy, G., Thasleema, SC., Ramkumar, T.K., and Sarojamma, B. “Selection of the best model for the rainfall data in India”, Mathematical Sciences International Research Journal, Vol. 1, Issue 3, pp.1033-1038, 2012.
  [8]. Jambhulkar, N. N. “Modeling of Rice Production in West Bengal”, International Journal of Scientific Research (IJSR), Vol. 2, Issue 7, pp. 9-10, 2013a.
  [9]. Jambhulkar, N. N. “Modeling of Rice Production in Punjab using ARIMA Model”, International Journal of Scientific Research (IJSR), Vol. 2, Issue 8, pp. 1-2, 2013b.
  [10]. Biswas, R. and Bhattacharyya, B. “ARIMA modeling to forecast area and production of rice in West Bengal”, Journal of Crop and Weed, Vol. 9, Issue 2, pp. 26-31, 2013.
  [11]. Prabakaran, K. and Sivapragasam, C. “Forecasting areas and production of rice in India using ARIMA model”, International Journal of Farm Sciences, Vol. 4, Issue 1, pp. 99-106, 2014.
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  Citation
  S. C. Thasleema, Ahammad Basha Shaik, "Stochastic Time Series Modeling for Rice Production in Andhra Pradesh," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.50-55, 2019

• Open Access   Article

  A Study of Mathematical Model for Pollutant Concentration and Dissolved Oxygen Concentration in the Kshipra River (India)

  A. Jain, V. H. Badshah, V. Gupta

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.56-60, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.5660

  Abstract

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  References

  Citation

  Abstract
  This paper addresses a mathematical model for pollutant and dissolved oxygen concentrations in a river. The physical and mass conservation laws governing the interaction of pollutant and dissolved oxygen are expressed as non-linear one-dimensional, time-dependent, coupled partial differential equations and are solved numerically, for zero-diffusion case, using fourth-order Runge-Kutta method. Time required for the pollutant to decay completely and dissolved oxygen to reach its saturation level is obtained graphically through simulation study. A particular case of the River Kshipra (Madhya Pradesh, India) is studied in detail. The result indicates the self-purification ability of the river at four different monitoring stations along its stretch in Ujjain city, using some standard parameters of water quality. The study is motivated by the pathetic condition of the river, as it receives large amount of untreated sewage daily. This study provides a better understanding of the complex phenomena of pollution transportation in the River Kshipra.

  Key-Words / Index Term
  Dissolved Oxygen, Biochemical Oxygen Demand, Diffusion, Advection, Runge-Kutta Method

  References
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  Citation
  A. Jain, V. H. Badshah, V. Gupta, "A Study of Mathematical Model for Pollutant Concentration and Dissolved Oxygen Concentration in the Kshipra River (India)," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.56-60, 2019