Fuzziness or uncertainties arise due to insufficient knowledge,experimental errors,operating conditions and parameters that provide inaccurate information.The concepts of susceptible,infectious and recovered are uncer...Fuzziness or uncertainties arise due to insufficient knowledge,experimental errors,operating conditions and parameters that provide inaccurate information.The concepts of susceptible,infectious and recovered are uncertain due to the different degrees in susceptibility,infectivity and recovery among the individuals of the population.The differences can arise,when the population groups under the consideration having distinct habits,customs and different age groups have different degrees of resistance,etc.More realistic models are needed which consider these different degrees of susceptibility infectivity and recovery of the individuals.In this paper,a Susceptible,Infected and Recovered(SIR)epidemic model with fuzzy parameters is discussed.The infection,recovery and death rates due to the disease are considered as fuzzy numbers.Fuzzy basic reproduction number and fuzzy equilibrium points have been derived for the studied model.Themodel is then solved numerically with three different techniques,forward Euler,Runge-Kutta fourth order method(RK-4)and the nonstandard finite difference(NSFD)methods respectively.The NSFD technique becomes more efficient and reliable among the others and preserves all the essential features of a continuous dynamical system.展开更多
基金The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project(Grant No.PNURSP2022R55),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘Fuzziness or uncertainties arise due to insufficient knowledge,experimental errors,operating conditions and parameters that provide inaccurate information.The concepts of susceptible,infectious and recovered are uncertain due to the different degrees in susceptibility,infectivity and recovery among the individuals of the population.The differences can arise,when the population groups under the consideration having distinct habits,customs and different age groups have different degrees of resistance,etc.More realistic models are needed which consider these different degrees of susceptibility infectivity and recovery of the individuals.In this paper,a Susceptible,Infected and Recovered(SIR)epidemic model with fuzzy parameters is discussed.The infection,recovery and death rates due to the disease are considered as fuzzy numbers.Fuzzy basic reproduction number and fuzzy equilibrium points have been derived for the studied model.Themodel is then solved numerically with three different techniques,forward Euler,Runge-Kutta fourth order method(RK-4)and the nonstandard finite difference(NSFD)methods respectively.The NSFD technique becomes more efficient and reliable among the others and preserves all the essential features of a continuous dynamical system.
