A Prey Predator Model in Case of Disease Transmission via Pest in Uncertain Environment.

Several diseases are transmitted from the infected individual to the uninfected one by different ways, like, pests, vectors, bacteria, viruses, etc. The living materials generally suffer from diseases some of which are contagious and the others are not infectious. There are lots of infectious diseases which are carried by the pests to the new individual to get infected after coming in touch of those particular pests. In this paper, a non-linear mathematical model is proposed to study the dynamics of disease transmission via pest among both components of susceptible prey and infected prey. The crisp model so formulated is converted to fuzzy model in which the control parameters are taken as triangular fuzzy numbers. The fuzzy model is reduced to the defuzzified model by using graded mean integration technique for defuzzification for triangular fuzzy number for the ease to find the solution. Also, the model is compared with fully stochastic model using a Markov process. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. Also, all the feasible equilibrium points are determined and local stability, global stability analysis and Hopf bifurcations are investigated. Further, a numerical experiment is done with the help of MATLAB packages. Finally, the sensitivities of the control parameters are studied and presented graphically from which the control of the disease transmission can be handled. [ABSTRACT FROM AUTHOR]