Parameter Sensitivity and Elasticity Analysis of a Mathematical Model for Non–Homogenous Population Density of a Weed Species (Published)
In this work, a stage-structured model for non- homogenous population density of an annual weed is analysed for parameter sensitivity and elasticity. The steady state solution of the model is obtained. In order to determine the contribution of identified parameters to the model steady state, the sensitivity and elasticity analyses are performed using matrix calculus approach. The result of the sensitivity analysis shows that the steady state is very responsive to change in established seedling survival rate (e). While, elasticity analysis indicates that, both established and matured weeds steady-state densities are equally affected by small additive changes in maturity rate (m) and establishment rate (e). Besides, seed bank seed density is most sensitive to small additive change in seed production (b) as compared to weed maturity rate (m). Hence, we conclude that increase in the survival and maturity rates possibly may lead to an increase in weed population density.
The main objective of this study is to estimate petroleum products demand using a random trend approach with aim of deriving improved and more robust estimates of price and income elasticities. The study specifies the random trend model of petroleum products demand as a two-step stochastic process. The estimates of model parameters for each petroleum products, in Nigeria are obtained by applying maximum likelihood in conjunction with Kalman filter. The study revealed that the introduction of random trend reduces the estimate of the coefficient of the lagged dependent variable in the three petroleum products relative to no trend model. As a result, price and income elasticities of petroleum product demands are higher in the short run and long run relative to constant intercept model. The introduction of random trend leads to improvement in the mean square errors of within sample forecasts