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

Das, Subhashis; Mahato, Prasenjit; Mahato, Sanat Kumar

doi:10.1007/s12591-020-00551-7

Cited by 7 publications

(1 citation statement)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Das and Pal ( 2018 ) proposed the imprecise epidemic system with optimal treatment and vaccination to control the epidemic. Researchers paid attention to develop the epidemic models in uncertain environments (Pontryagin et al 1962 ; Panja et al 2017 ; Mahata et al 2018 ; Nandi et al 2018 ; Das et al 2020a ). Das et al ( 2020b ) explained disease control eco-epidemic model with prey refuge under fuzzy uncertainty.…”

Section: Introductionmentioning

confidence: 99%

An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness

Mahato

Das

Mahato

2021

Model. Earth Syst. Environ.

Self Cite

View full text Add to dashboard Cite

In this work, we propose a nonlinear susceptible ( S ), vaccinated ( V ), infective ( I ), recovered ( R ), information level ( U ) (SVIRUS) model for the dynamical behavior of the contagious disease in human beings. We mainly consider the spread of information during the course of epidemic in the population. Different rate equations describe the dynamics of the information. We have developed the proposed model in crisp and fuzzy environments. In the fuzzy model, to describe the uncertainty prevailed in the dynamics, all the parameters are taken as triangular fuzzy numbers. Using graded mean integration value (GMIV) method, the fuzzy model is transformed into defuzzified model to represent the solutions avoiding the difficulties. The positivity and the boundedness of the crisp model are discussed elaborately and also the equilibrium analysis is accomplished. The stability analysis for both the infection free and the infected equilibrium are established for the crisp model. Application of optimal control of the crisp system is explored. Using Pontryagin’s Maximum Principle, the optimal control is explained. The effect of vaccination is analyzed which leads the model to be complex in nature. The effect of saturation constant for information is described for the crisp model and also the effects of weight constants on control policy are discussed. Finally, it is concluded that the treatment is more fruitful and information related vaccination is more effective during the course of epidemic.

show abstract