A Prey Predator Model in Case of Disease Transmission via Pest in Uncertain Environment
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A Prey Predator Model in Case of Disease Transmission via Pest in Uncertain Environment Subhashis Das1 · Prasenjit Mahato1 · Sanat Kumar Mahato1
© Foundation for Scientific Research and Technological Innovation 2020
Abstract 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. Keywords Disease transmission · Graded mean integration value · Defuzzification · Global stability · Asymptotically stable
* Subhashis Das [email protected] Prasenjit Mahato [email protected] Sanat Kumar Mahato [email protected] 1
Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, West Bengal 723104, India
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Vol.:(0123456789)
Differential Equations and Dynamical Systems
Introduction Several diseases are transmitted from person to person by direct or indirect contact. Certain types of viruses, bacteria, pests, vectors and fungi can cause infectious disease. Malaria, measles and respiratory illnesses are examples of infectious diseases. The living things generally suffer from diseases, some of which are contagious and the others are not. The infectious diseases are transmitted by the pests to the new individual. Pests are major threat to health worldwide. The economic implications of these diseases are also immense in both developing and developed countries. In developing countries, large proportions of the population suffer overwhelming health services, debilitating diseases. The effect of those pests can cause not only on humans and animals but also it harms the plants. So, it is easy to understand why the control of the pest is one of the biggest problems. The first step forward in modern mathematical ecology was do
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