Asian Journal of Probability and Statistics

This work, presents a formulation of mathematical model of bird harvesting in an intensive poultry system, under the assumption that under a favourable environmental atmosphere and good management system, the birds have logistic growth. The model is analysed using methods from dynamical system theory and theory of calculus. It was established that the system has two steady state, the two equilibrium state are both locally asymptotically stable. The first one is stable if there is a bound on the harvest rate of the birds, which is proportional to the growth rate of the birds. The second equilibrium state is locally asymptotically stable (LAS)  if  k < \(\frac{r(C+y)}{p}\) that is if the carrying capacity is less than   the ratio of the sum of and Per unit tax on the bird to that of Per unit price of the birds. Further analysis indicates that the limiting population of bird, that is the maximum population of birds that the available resources in the system can sustain and also ensures harvesting profitability is given as $${k(r-{kp (r-\mu) -r(c+y) \over kp}- \mu}\over kp $$
This occurs at the point (\(\bar{t}\),\(\bar{B}\)) = 
\(\left(\left(\frac{1}{\left(r-\beta\left(\frac{K \rho(r-\mu)-r(\mathrm{C}+\gamma)}{K \rho}\right)-\mu\right)} \operatorname{Ln}\left(\frac{\frac{K\left(r-\frac{K \rho(r-\mu)-r(\mathrm{C}+\gamma)}{K \rho}-\mu\right)}{r}-\mathrm{B}_0}{\mathrm{~B}_0}\right),\left(\frac{K\left(r-\frac{K \rho(r-\mu)-r(\mathrm{C}+\gamma)}{K \rho}-\mu\right)}{2 r}\right)\right)\right.\)