Research Article Different Solution Strategies for Solving Epidemic Model in Imprecise Environment Animesh Mahata , 1,2 Sankar Prasad Mondal , 3 Ali Ahmadian , 4 Fudiah Ismail , 4 Shariful Alam, 1 and Soheil Salahshour 5 1 Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India 2 Department of Mathematics, Netaji Subhash Engineering College, Techno City, Garia, Kolkata, West Bengal 700152, India 3 Department of Mathematics, Midnapore College (Autonomous), Midnapore, West Midnapore, West Bengal 721101, India 4 Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia 5 Young Researchers and Elite Club, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Iran Correspondence should be addressed to Ali Ahmadian; ahmadian.hosseini@gmail.com Received 6 February 2017; Revised 6 June 2017; Accepted 15 January 2018; Published 13 May 2018 Academic Editor: Carla Pinto Copyright © 2018 Animesh Mahata et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We study the diferent solution strategy for solving epidemic model in diferent imprecise environment, that is, a Susceptible- Infected-Susceptible (SIS) model in imprecise environment. Te imprecise parameter is also taken as fuzzy and interval environment. Tree diferent solution procedures for solving governing fuzzy diferential equation, that is, fuzzy diferential inclusion method, extension principle method, and fuzzy derivative approaches, are considered. Te interval diferential equation is also solved. Te numerical results are discussed for all approaches in diferent imprecise environment. 1. Introduction 1.1. Modeling with Impreciseness. Te aim of mathematical modeling is to imitate some real world problems as far as pos- sible. Te presence of imprecise variable and parameters in practical problems in the feld of biomathematical modeling became a new area of research in uncertainty modeling. So, the solution procedure of such problems is very important. If the solution of said problems with uncertainty is developed, then, many real life models in diferent felds with imprecise variable can be formulated and solved easily and accurately. 1.2. Fuzzy Set Teory and Diferential Equation. Diferential equations may arise in the mathematical modeling of real world problems. But when the impreciseness comes to it, the behavior of the diferential equation is altered. Te solution procedures are taken in diferent way. In this paper we take two types of imprecise environments, fuzzy and interval, and fnd their exact solution. In 1965, Zadeh [1] published the frst of his papers on the new theory of Fuzzy Sets and Systems. Afer that Chang and Zadeh [2] introduced the concept of fuzzy numbers. In the last few years researchers have been giving their great contribution on the topic of fuzzy number research [3–5]. As for the application of the fuzzy set theory applied in fuzzy equation [6], fuzzy diferential equation [7], fuzzy integrodiferential equation [8–10], fuzzy integral equation [11], and so on were developed. 1.3. Diferent Approaches for Solving Fuzzy Diferential Equa- tion. Te application of diferential equations has been widely explored in various felds like engineering, economics, biology, and physics. For constructing diferent types of problems in real life situation the fuzzy set theory plays an important role. Te applicability of nonsharp or imprecise concept is very useful for exploring diferent sectors for its applicability. A diferential equation can be called fuzzy diferential equation if (1) only the coefcient (or coefcients) of the diferential equation is fuzzy valued number, (2) only Hindawi Complexity Volume 2018, Article ID 4902142, 18 pages https://doi.org/10.1155/2018/4902142