Complex Dynamics of Some Ecological Systems. With Special Emphasis on Epidemiological Problems

      Аннотация: The present book deals with some mathematical models on ecological and epidemiological problems. To explore ecological aspects, different models on prey-predator system like stage structured predator-prey system, prey-predator system incorporating a prey-refuge are formulated and extensively studied. Some prey-predator models where prey populations are attacked by parasite of some infectious diseases are also proposed and analyzed thoroughly. Agricultural pest control system is an extensive example of that type system and we describe a model to control pest population. Some mathematical models on infectious diseases related to human society are also developed and analyzed. We take help of first order ordinary differential equation and delay differential equations to formulate the models. A detailed dynamical behavior of each of the models is studied. Different mathematical tools like qualitative theory of ordinary differential equations, delay differential equations, bifurcation theory, geometric approach, optimization techniques, numerical analysis and control theory are used to analyze the models mathematically and relate them with biological phenomena.

Ключевые слова: bifurcation theory, delay, Mathematical model, Optimal Control Theory, Simulation, Stability Theory, differential equation