Eco-Epidemiological Modelling and Analysis of Prey-Predator Population
Abayneh Fentie Bezabih,
Geremew Kenassa Edessa,
Koya Purnachandra Rao
Issue:
Volume 9, Issue 1, February 2021
Pages:
1-14
Received:
10 November 2020
Accepted:
4 December 2020
Published:
23 February 2021
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.
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 th...
Show More
Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data
Elgabry Gamalat,
Rezk Hoda
Issue:
Volume 9, Issue 1, February 2021
Pages:
15-19
Received:
22 January 2021
Accepted:
7 February 2021
Published:
23 February 2021
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.
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...
Show More
Nonparametric Penalized Spline Model Calibrated Estimator in Complex Survey with Known Auxiliary Information at Both Cluster and Element Levels
Nthiwa Janiffer Mwende,
Ali Salim Islam,
Pius Nderitu Kihara
Issue:
Volume 9, Issue 1, February 2021
Pages:
20-32
Received:
27 November 2020
Accepted:
16 February 2021
Published:
10 March 2021
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 the population total. The calibration problems at both levels have been treated as optimization problems and solved using penalty functions to derive the estimators for this study. The reasoning behind model calibration is that if the calibration constraints are satisfied by the auxiliary variable, the study expects that the variable of interest’s fitted values meets such constraints. This study runs 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 if the model is misspecified for the data.
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 a...
Show More
