Pub Date : 2021-07-24DOI: 10.11648/J.SJAMS.20210903.13
Bantie Getnet, Kinfe Gebrekrstos, Lidet Dereje
In Ethiopia, small scale farmers contribute about 80% of the total population of the country and their land holding and also small, that farmer cannot allow the land to stay follow. Some developing region in the country is not fully benefit from the opportunities that can be generated by farm investment project. The study investigates the quality of life of people in near to Woldia town. The main objective of this study was to assess the impact of farm-investment on farmers’ quality of life in near to Woldia town. The appropriate methodology to meet sample size in this study was obtained by using simple random sampling techniques which gives equal chance to every members of population to be selected as a sample. The data was analyzed by using both descriptive and inferential statistics. And the model used for this study was binary logistic regression used to analysis the inferential statistics. And also chi-square used for testing association between dependent and independent variables like gender, marital status, family income, and occupation. This study also identifies gender, occupation, family income; marital status and educational level have impact on quality of life. Finally, the study recommended that the advantage of investments for farmers such as employment opportunities, construction of different social services like school, health center, and economic development to bring a families good quality of life.
{"title":"Assessing the Impacts of Farm-investment on Farmer’s Quality of Life in Near to Woldia Town, North Wollo Ethiopia","authors":"Bantie Getnet, Kinfe Gebrekrstos, Lidet Dereje","doi":"10.11648/J.SJAMS.20210903.13","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20210903.13","url":null,"abstract":"In Ethiopia, small scale farmers contribute about 80% of the total population of the country and their land holding and also small, that farmer cannot allow the land to stay follow. Some developing region in the country is not fully benefit from the opportunities that can be generated by farm investment project. The study investigates the quality of life of people in near to Woldia town. The main objective of this study was to assess the impact of farm-investment on farmers’ quality of life in near to Woldia town. The appropriate methodology to meet sample size in this study was obtained by using simple random sampling techniques which gives equal chance to every members of population to be selected as a sample. The data was analyzed by using both descriptive and inferential statistics. And the model used for this study was binary logistic regression used to analysis the inferential statistics. And also chi-square used for testing association between dependent and independent variables like gender, marital status, family income, and occupation. This study also identifies gender, occupation, family income; marital status and educational level have impact on quality of life. Finally, the study recommended that the advantage of investments for farmers such as employment opportunities, construction of different social services like school, health center, and economic development to bring a families good quality of life.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124847958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-26DOI: 10.11648/J.SJAMS.20210903.11
Randhir Singh
Loss functions and Risk functions play very important role in Bayesian estimation. This paper aims at the Bayesian estimation for the loss and risk functions of the unknown parameter of the H(r, theta), (theta being the unknown parameter) distribution The estimation has been performed under Rukhin’s loss function. The importance of this distribution is that it contains some important distributions such as the Half Normal distribution, Rayleigh distribution and Maxwell’s distribution as particular cases. The inverse Gamma distribution has assumed as the prior distribution for the unknown parameter theta. This prior distribution is a Natural Conjugate prior distribution for the unknown parameter because the posterior probability density function of the unknown parameter is also inverse gamma distribution The Rukhin’s loss function involves another loss function denoted by w(theta, delta) he form of w(theta, delta) is important as it changes the estimate. In this paper, three forms of w(theta, delta) have been taken and corresponding estimates have been derived. The three, forms are, the Squared Error Loss Function (SELF) and two different forms of Weighted Squared Error Loss Function (WSELF) namely, the Minimum Expected Loss (MELO) Function and the Exponentially Weighted Minimum Expected Loss (EWMELO) Function have been considered. A criterion of performance of various form of w(theta, delta) has ben defined. It has been proved that among three forms of w(theta, delta), considered here, the form corresponding to EWMELO is most dominant.
{"title":"On Bayesian Estimation of Loss and Risk Functions","authors":"Randhir Singh","doi":"10.11648/J.SJAMS.20210903.11","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20210903.11","url":null,"abstract":"Loss functions and Risk functions play very important role in Bayesian estimation. This paper aims at the Bayesian estimation for the loss and risk functions of the unknown parameter of the H(r, theta), (theta being the unknown parameter) distribution The estimation has been performed under Rukhin’s loss function. The importance of this distribution is that it contains some important distributions such as the Half Normal distribution, Rayleigh distribution and Maxwell’s distribution as particular cases. The inverse Gamma distribution has assumed as the prior distribution for the unknown parameter theta. This prior distribution is a Natural Conjugate prior distribution for the unknown parameter because the posterior probability density function of the unknown parameter is also inverse gamma distribution The Rukhin’s loss function involves another loss function denoted by w(theta, delta) he form of w(theta, delta) is important as it changes the estimate. In this paper, three forms of w(theta, delta) have been taken and corresponding estimates have been derived. The three, forms are, the Squared Error Loss Function (SELF) and two different forms of Weighted Squared Error Loss Function (WSELF) namely, the Minimum Expected Loss (MELO) Function and the Exponentially Weighted Minimum Expected Loss (EWMELO) Function have been considered. A criterion of performance of various form of w(theta, delta) has ben defined. It has been proved that among three forms of w(theta, delta), considered here, the form corresponding to EWMELO is most dominant.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125043430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-07DOI: 10.11648/J.SJAMS.20210902.13
Melissa Innerst, J. Tubbs, M. Ghebremichael
Recently, several regression methods have been developed to model the receiver operating characteristic curve (ROC), as a measure of accuracy for potential biomarker use in diagnostic testing and disease detection. In this paper, we investigate the Lehmann ROC regression model and compare it to more commonly used ROC regression methods that are found in the literature. The comparative performance of the methods are evaluated using simulated data from the normal, extreme value, and the Weibull distributions. Theory suggests that the Lehmann method should only work well when using the Weibull distribution. Our simulation results suggest that the performance of these methods is more complicated than the theory might suggest. The methods were demonstrated using data from a study concerning the clinical effectiveness of leukocyte elastase determination in the diagnosis of coronary artery disease (CAD).
{"title":"A Comparison of the Lehmann and GLM ROC Models","authors":"Melissa Innerst, J. Tubbs, M. Ghebremichael","doi":"10.11648/J.SJAMS.20210902.13","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20210902.13","url":null,"abstract":"Recently, several regression methods have been developed to model the receiver operating characteristic curve (ROC), as a measure of accuracy for potential biomarker use in diagnostic testing and disease detection. In this paper, we investigate the Lehmann ROC regression model and compare it to more commonly used ROC regression methods that are found in the literature. The comparative performance of the methods are evaluated using simulated data from the normal, extreme value, and the Weibull distributions. Theory suggests that the Lehmann method should only work well when using the Weibull distribution. Our simulation results suggest that the performance of these methods is more complicated than the theory might suggest. The methods were demonstrated using data from a study concerning the clinical effectiveness of leukocyte elastase determination in the diagnosis of coronary artery disease (CAD).","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"150 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115114238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-30DOI: 10.11648/J.SJAMS.20210902.12
A. Mohamed, A. Elghany, Gamalat Elgabry
In this paper, we consider power odd generalized exponential-Gompertz (POGE-G) distribution which is capable of life tables to calculate death rates (failure). Based on simulated data from the PPOGE-G distribution, we consider the problem of estimation of parameters under classical approaches and Bayesian approaches. In this regard, we obtain maximum likelihood (ML) estimates, maximum product of spacing (MPS) and Bayes estimates under squared error loss function. We also compute 95% asymptotic confidence interval and highest posterior density interval estimates. The Monte Carlo simulation will be conduct to study and compare the performance of the various proposed estimators (simulation study indicates that the performance of MPS estimates is better MLE estimates and the performance of Bayes estimates is also better). Finally, application of a real data from the projections of the future population for the total of the Egyptian Arabic Republic for the period 2017-2052, depending on the book which introduced from the central agency for public mobilization and statistics in Feb (2019) from this application it could be said that this distributions can be applied to mortality rate data set. The present paper can also be extended to design of progressive censoring sampling plan and other censoring schemes can also be considered.
{"title":"Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates","authors":"A. Mohamed, A. Elghany, Gamalat Elgabry","doi":"10.11648/J.SJAMS.20210902.12","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20210902.12","url":null,"abstract":"In this paper, we consider power odd generalized exponential-Gompertz (POGE-G) distribution which is capable of life tables to calculate death rates (failure). Based on simulated data from the PPOGE-G distribution, we consider the problem of estimation of parameters under classical approaches and Bayesian approaches. In this regard, we obtain maximum likelihood (ML) estimates, maximum product of spacing (MPS) and Bayes estimates under squared error loss function. We also compute 95% asymptotic confidence interval and highest posterior density interval estimates. The Monte Carlo simulation will be conduct to study and compare the performance of the various proposed estimators (simulation study indicates that the performance of MPS estimates is better MLE estimates and the performance of Bayes estimates is also better). Finally, application of a real data from the projections of the future population for the total of the Egyptian Arabic Republic for the period 2017-2052, depending on the book which introduced from the central agency for public mobilization and statistics in Feb (2019) from this application it could be said that this distributions can be applied to mortality rate data set. The present paper can also be extended to design of progressive censoring sampling plan and other censoring schemes can also be considered.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"17 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133408611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-17DOI: 10.11648/J.SJAMS.20210902.11
Otieno Okumu Kevin, Samuel Muthiga Nganga
After the establishment of the Narok County government and the transition from the central system of government into the Devolved system of governance, majority of the residents of Narok County had much anticipation in terms of developments that will take place as a result of governance being brought close to them. The study was checking economic development changes that has taken place in Narok Town the Headquarter of Narok County since the establishment of the Narok County Government. The objective was to access how the introduction of county government has impacted on the economic development by investigating its impact on the various key indicators of the economic development such as health, trade, and infrastructure. The study used a sample of 320 residents drawn at random from all parts of the town, the samples was surveyed using a written survey instrument and their opinion on the state of various economic indicators was captured and used to develop a structural equation model using SmartPLS 3 software, in order to use in examining the economic development status of Narok Town. The study fits a significant model that can tell the whereabouts of the economic status of the Town presently and in future. It was concluded that the county government has not done much in terms of economic development since the introduction of County government because the rural areas in the county are still struggling to catch up with the indicators of economic development. It was also evidenced that the impact of County government on trade is good compared to its impact on health and infrastructure.
{"title":"Analyzing the Economic Development Using Partial Least Square Structural Model: A Case of Narok, Kenya","authors":"Otieno Okumu Kevin, Samuel Muthiga Nganga","doi":"10.11648/J.SJAMS.20210902.11","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20210902.11","url":null,"abstract":"After the establishment of the Narok County government and the transition from the central system of government into the Devolved system of governance, majority of the residents of Narok County had much anticipation in terms of developments that will take place as a result of governance being brought close to them. The study was checking economic development changes that has taken place in Narok Town the Headquarter of Narok County since the establishment of the Narok County Government. The objective was to access how the introduction of county government has impacted on the economic development by investigating its impact on the various key indicators of the economic development such as health, trade, and infrastructure. The study used a sample of 320 residents drawn at random from all parts of the town, the samples was surveyed using a written survey instrument and their opinion on the state of various economic indicators was captured and used to develop a structural equation model using SmartPLS 3 software, in order to use in examining the economic development status of Narok Town. The study fits a significant model that can tell the whereabouts of the economic status of the Town presently and in future. It was concluded that the county government has not done much in terms of economic development since the introduction of County government because the rural areas in the county are still struggling to catch up with the indicators of economic development. It was also evidenced that the impact of County government on trade is good compared to its impact on health and infrastructure.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115007640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-10DOI: 10.11648/J.SJAMS.20210901.13
Nthiwa Janiffer Mwende, A. Islam, Pius Nderitu Kihara
The present study uses penalized splines (p- spline) to estimate the functional relationship between the survey variable and the auxiliary variable in a complex survey design; where a population divided into clusters is in turn subdivided into strata. This study has considered a case of auxiliary information present at two levels; at both cluster and element levels. The study further, applied model calibration technique by penalty function to estimate population total. The calibration problems at both levels have been treated as optimization problems and solving by the method of penalty functions so as to derive the estimators for this study. The reasoning behind the use of model calibration is that if the calibration constraints are satisfied by the auxiliary variable, then the study expects that the fitted values of the variable of interest satisfies such constraints too. This study run a Monte Carlo simulation to assess the finite sample performance of the penalized spline model calibrated estimator under complex survey data. Simulation studies were conducted to compare the efficiency of p-spline model calibrated estimator with Horvitz Thompson estimator (HT) by mean squared error (MSE) criterion. This study shows that the p-spline model-based estimator is generally more efficient than the HT in terms of the mean squared error. The results have also shown that the estimator obtained is unbiased, consistent and very robust because it does not fail in the event the model is misspecified for the data.
{"title":"Nonparametric Penalized Spline Model Calibrated Estimator in Complex Survey with Known Auxiliary Information at Both Cluster and Element Levels","authors":"Nthiwa Janiffer Mwende, A. Islam, Pius Nderitu Kihara","doi":"10.11648/J.SJAMS.20210901.13","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20210901.13","url":null,"abstract":"The present study uses penalized splines (p- spline) to estimate the functional relationship between the survey variable and the auxiliary variable in a complex survey design; where a population divided into clusters is in turn subdivided into strata. This study has considered a case of auxiliary information present at two levels; at both cluster and element levels. The study further, applied model calibration technique by penalty function to estimate population total. The calibration problems at both levels have been treated as optimization problems and solving by the method of penalty functions so as to derive the estimators for this study. The reasoning behind the use of model calibration is that if the calibration constraints are satisfied by the auxiliary variable, then the study expects that the fitted values of the variable of interest satisfies such constraints too. This study run a Monte Carlo simulation to assess the finite sample performance of the penalized spline model calibrated estimator under complex survey data. Simulation studies were conducted to compare the efficiency of p-spline model calibrated estimator with Horvitz Thompson estimator (HT) by mean squared error (MSE) criterion. This study shows that the p-spline model-based estimator is generally more efficient than the HT in terms of the mean squared error. The results have also shown that the estimator obtained is unbiased, consistent and very robust because it does not fail in the event the model is misspecified for the data.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114426827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-23DOI: 10.11648/J.SJAMS.20210901.12
Elgabry Gamalat, Rezk Hoda
As a result of technology improvement getting information about products and materials lifetimes under usual conditions. Therefore accelerated life testing or partially accelerated life testing usually are used to truncate the tests survives. The test items under accelerated life testing run under accelerated conditions and partially life tests run under both accelerated and use conditions. The main idea of accelerated life testing that the acceleration element is not unknown or the mathematical model relating the lifetime of the unit and the stress is known or can be assumed. In some cases, neither acceleration factor nor life-stress relations are not unknown. This paper concerned with studying and discussed the constant–stress partially accelerated life test (CPALT) under type I censored (T.I.C) competing risks data. Failure times resulting from T.I.C competing risks data are assumed to follow the Extended generalized log logistic (EGLL) distribution because this model is completely flexible to study positive data. This distribution is applied in various fields, for example lifetime studies, economics, finance and insurance. The maximum likelihood (ML) method is used to estimate the parameters under TIC competing risks data. The simulation algorithm is performed to assess the theoretical results of the maximum likelihood estimates based on TIC competing risks data.
{"title":"Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data","authors":"Elgabry Gamalat, Rezk Hoda","doi":"10.11648/J.SJAMS.20210901.12","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20210901.12","url":null,"abstract":"As a result of technology improvement getting information about products and materials lifetimes under usual conditions. Therefore accelerated life testing or partially accelerated life testing usually are used to truncate the tests survives. The test items under accelerated life testing run under accelerated conditions and partially life tests run under both accelerated and use conditions. The main idea of accelerated life testing that the acceleration element is not unknown or the mathematical model relating the lifetime of the unit and the stress is known or can be assumed. In some cases, neither acceleration factor nor life-stress relations are not unknown. This paper concerned with studying and discussed the constant–stress partially accelerated life test (CPALT) under type I censored (T.I.C) competing risks data. Failure times resulting from T.I.C competing risks data are assumed to follow the Extended generalized log logistic (EGLL) distribution because this model is completely flexible to study positive data. This distribution is applied in various fields, for example lifetime studies, economics, finance and insurance. The maximum likelihood (ML) method is used to estimate the parameters under TIC competing risks data. The simulation algorithm is performed to assess the theoretical results of the maximum likelihood estimates based on TIC competing risks data.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122329469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-23DOI: 10.11648/J.SJAMS.20210901.11
Abayneh Fentie Bezabih, G. K. Edessa, Koya Purnachandra Rao
In this paper, prey-predator model of five Compartments are constructed with treatment is given to infected prey and infected predator. We took predation incidence rates as functional response type II and disease transmission incidence rates follow simple kinetic mass action function. The positivity, boundedness, and existence of the solution of the model are established and checked. Equilibrium points of the models are identified and Local stability analysis of Trivial Equilibrium point, Axial Equilibrium point, and Disease-free Equilibrium points are performed with the Method of Variation Matrix and Routh Hourwith Criterion. It is found that the Trivial equilibrium point 〖E〗_(o) is always unstable, and Axial equilibrium point 〖E〗_(A) is locally asymptotically stable if βk - (t1+d2) < 0, qp1k - d3(s+k) < 0, & qp3k - (t2+d4)(s+k) < 0 conditions hold true. Global Stability analysis of endemic equilibrium point of the model has been proved by Considering appropriate Liapunove function. In this study, the basic reproduction number of infected prey is obtained to be the following general formula R01=[(qp1-d3)2 kβd3s2]⁄[(qp1-d3){(qp1-d3)2ks(t1+d2 )+rsqp2 (kqp1-kd3-d3s)}] and the basic reproduction number of infected predator population is computed and results are written as the general formula of the form as R02=[(qp1-d3 )(qp3 d3 )k+αrsq(kqp1-kd3-d3s)]⁄[(qp1-d3)2 (t2+d4)k]. If the basic reproduction number is greater than one, then the disease will persist in prey-predator system. If the basic reproduction number is one, then the disease is stable, and if basic reproduction number less than one, then the disease is dies out from the prey-predator system. Finally, simulations are done with the help of DEDiscover software to clarify results.
{"title":"Eco-Epidemiological Modelling and Analysis of Prey-Predator Population","authors":"Abayneh Fentie Bezabih, G. K. Edessa, Koya Purnachandra Rao","doi":"10.11648/J.SJAMS.20210901.11","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20210901.11","url":null,"abstract":"In this paper, prey-predator model of five Compartments are constructed with treatment is given to infected prey and infected predator. We took predation incidence rates as functional response type II and disease transmission incidence rates follow simple kinetic mass action function. The positivity, boundedness, and existence of the solution of the model are established and checked. Equilibrium points of the models are identified and Local stability analysis of Trivial Equilibrium point, Axial Equilibrium point, and Disease-free Equilibrium points are performed with the Method of Variation Matrix and Routh Hourwith Criterion. It is found that the Trivial equilibrium point 〖E〗_(o) is always unstable, and Axial equilibrium point 〖E〗_(A) is locally asymptotically stable if βk - (t1+d2) < 0, qp1k - d3(s+k) < 0, & qp3k - (t2+d4)(s+k) < 0 conditions hold true. Global Stability analysis of endemic equilibrium point of the model has been proved by Considering appropriate Liapunove function. In this study, the basic reproduction number of infected prey is obtained to be the following general formula R01=[(qp1-d3)2 kβd3s2]⁄[(qp1-d3){(qp1-d3)2ks(t1+d2 )+rsqp2 (kqp1-kd3-d3s)}] and the basic reproduction number of infected predator population is computed and results are written as the general formula of the form as R02=[(qp1-d3 )(qp3 d3 )k+αrsq(kqp1-kd3-d3s)]⁄[(qp1-d3)2 (t2+d4)k]. If the basic reproduction number is greater than one, then the disease will persist in prey-predator system. If the basic reproduction number is one, then the disease is stable, and if basic reproduction number less than one, then the disease is dies out from the prey-predator system. Finally, simulations are done with the help of DEDiscover software to clarify results.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121682360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The production and productivity of field pea in Ethiopia is constrained by low-yielding potential of land race, susceptibility to diseases like powdery mildew and Ascochyta blight/spot as well as a biotic stresses like frost and soil acidity. The field experiment was conducted in 2018/19 main cropping season at two locations using simple lattice design to evaluate the genetic variability and performance of forty nine field pea genotypes for yield ad yield attributing traits. The combined/pooled / analysis of variance revealed highly significant (P≤0.01) to significant (P≤0.05) differences among genotypes observed for all traits under study except for number of seeds pod-1. The seed yield ranged from 1955 to 5997 kg ha-1 with a mean of 3803 kg across the two locations. Two genotypes PDFPT-BEK and P-313-053 were relatively high yielder over the two locations. The genotypic (GCV) and phenotypic (PCV) coefficient of variation (GCV) ranged from (1.07%) to (22.40%) and (1.22%) to (28.18% for days to maturity and grain yield, respectively for combined analyses. The PCV values were relatively greater than GCV in magnitude for all traits, of which significantly higher PCV than GCV values observed for number of pods per plant, Stand count, powdery mildew and ascocayta blight, but insignificant differences between PCV and GCV values observed for days to flowering, days to maturity, plant height, 1000 seed weight, and grain yield. Broad sense heritability ranged from 23.66% to 90.73%. The genetic advance as percentage of mean (GAM) varied from 1.92% to 36.73%. Higher heritability (H2) coupled with high GAM observed for grain yield per ha and Higher heritability (H2) coupled with Moderate or relatively high value of GAM in plant height and seed size. Therefore, improvement of these traits could be done through selection of genotypes based on the phenotypic performance.
{"title":"Evaluation of Field Pea (Pisum sativum L.) Genotypes for Yield and Yield Attributing Traits at High Land of Arsi, South East Ethiopia","authors":"Kedir Yimam, Aliyi Robsa, Gizachew Yilma, Temesgen Abo","doi":"10.11648/J.SJAMS.20200806.11","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20200806.11","url":null,"abstract":"The production and productivity of field pea in Ethiopia is constrained by low-yielding potential of land race, susceptibility to diseases like powdery mildew and Ascochyta blight/spot as well as a biotic stresses like frost and soil acidity. The field experiment was conducted in 2018/19 main cropping season at two locations using simple lattice design to evaluate the genetic variability and performance of forty nine field pea genotypes for yield ad yield attributing traits. The combined/pooled / analysis of variance revealed highly significant (P≤0.01) to significant (P≤0.05) differences among genotypes observed for all traits under study except for number of seeds pod-1. The seed yield ranged from 1955 to 5997 kg ha-1 with a mean of 3803 kg across the two locations. Two genotypes PDFPT-BEK and P-313-053 were relatively high yielder over the two locations. The genotypic (GCV) and phenotypic (PCV) coefficient of variation (GCV) ranged from (1.07%) to (22.40%) and (1.22%) to (28.18% for days to maturity and grain yield, respectively for combined analyses. The PCV values were relatively greater than GCV in magnitude for all traits, of which significantly higher PCV than GCV values observed for number of pods per plant, Stand count, powdery mildew and ascocayta blight, but insignificant differences between PCV and GCV values observed for days to flowering, days to maturity, plant height, 1000 seed weight, and grain yield. Broad sense heritability ranged from 23.66% to 90.73%. The genetic advance as percentage of mean (GAM) varied from 1.92% to 36.73%. Higher heritability (H2) coupled with high GAM observed for grain yield per ha and Higher heritability (H2) coupled with Moderate or relatively high value of GAM in plant height and seed size. Therefore, improvement of these traits could be done through selection of genotypes based on the phenotypic performance.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129207542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-29DOI: 10.11648/J.SJAMS.20200805.13
T. Tulu, I. Leong, Zunyou Wu
The COVID-19 pandemic is a global pandemic of coronavirus disease 2019, caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV 2). The outbreak was first identified in Wuhan, China, in December 2019. In this article, we investigate the problem of modelling the trend of the current Coronavirus disease 2019 pandemic in China, USA, Ethiopia and Brazil along time. Two different models were developed using Bayesian Markov chain Monte Carlo simulation methods. The models fitted included Poisson autoregressive as a function of a short-term dependence only and Poisson autoregressive as a function of both a short-term dependence and a long-term dependence. The models can be employed to understand the contagion dynamics of the COVID-19, which can heavily impact health, economy and finance. The result indicates whether disease has an upward/downward trend, and where about every country is on that trend, all of which can help the public decision-makers to better plan health policy interventions and take the appropriate actions to control the spreading of the virus.
{"title":"Modeling and Predicting Corona Contagion Dynamics in China, USA, Brazil & Ethiopia","authors":"T. Tulu, I. Leong, Zunyou Wu","doi":"10.11648/J.SJAMS.20200805.13","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20200805.13","url":null,"abstract":"The COVID-19 pandemic is a global pandemic of coronavirus disease 2019, caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV 2). The outbreak was first identified in Wuhan, China, in December 2019. In this article, we investigate the problem of modelling the trend of the current Coronavirus disease 2019 pandemic in China, USA, Ethiopia and Brazil along time. Two different models were developed using Bayesian Markov chain Monte Carlo simulation methods. The models fitted included Poisson autoregressive as a function of a short-term dependence only and Poisson autoregressive as a function of both a short-term dependence and a long-term dependence. The models can be employed to understand the contagion dynamics of the COVID-19, which can heavily impact health, economy and finance. The result indicates whether disease has an upward/downward trend, and where about every country is on that trend, all of which can help the public decision-makers to better plan health policy interventions and take the appropriate actions to control the spreading of the virus.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114089984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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