Bijal M. Yeolekar

Mathematical Analysis of Optimal Control Theory on Underweight

To achieve increase in the number of healthy people in the society, proper information and understanding about health care issues is required. This will bring about improvement and betterment of the health of the population, especially to the girls and women of the society who are welcoming the new generation. Females need to take an adequate amount of healthy and nutritive food in their daily life for themselves as well as for the development and well-being of the new generation so as to prevent malnutrition and underweight which may cause deficiency in the various parts and organs of the body. In this paper, we want to study the transmission of malnutrition and underweight individuals in the society. The strategy in terms of healthy life campaign and treatment for healthy individual in the society is focussed. The model is supported with numerical simulation.

Threshold for vaccination in measles and its vertical transmission

This study analyses measles transmission vertically with vaccination failure and delay of vaccination. The effect of infected newborns as a time delay is analysed. Time delay is considered as a loss of maternal immunity amongst newborns. The system of non-linear differential equations for the proposed problem is formulated. The next generation matrix method is used to find the reproduction number, and to obtain the stability of the infection free as well as the endemic equilibrium. Effect of time delay in vaccination has been studied for disease-free equilibrium. The local and global stability of the system is analysed. Sensitivity of the key parameters is measured using numerical simulation and observed that it supports the analytical results.

Optimal Fish Harvesting with Deterioration, Effort and PriceSensitive Demand

The dynamics of a fishery resource system is formulated for fish harvesting with effort and price-sensitive demand. The model considers deterioration as damage during catchability. It is assumed that the supply is instantaneous. The system of non-linear differential equations is formulated and solved to determine the non-trivial equilibrium. The conditions for stability of equilibria are worked out. The numerical data are used to support theoretical results derived.