In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria tran...In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (<img src="Edit_bced8210-1c24-4e78-bb5b-60ea7d37361c.png" alt="" /></span><span></span><span style="font-family:Verdana;">)</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> we reach the model disease-free equilibrium. Using Choquet integral</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Infected</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Recovered</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> susceptible-Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium <img src="Edit_cc2d122d-7c04-4fb7-a96a-3eb919a3785d.png" alt="" /> </span><span style="font-family:Verdana;">is globally asymptotically stable if <img src="Edit_0974e52f-cf63-4bfa-9781-1ebce366a4a3.png" alt="" /></span><span></span><span style="font-family:Verdana;"> or if the basic reproduction number is less than one (<img src="Edit_dbffcb03-cd00-4213-b7e1-ada9a0cf5c98.png" alt="" /></span><span></span><span style="font-family:Verdana;">). When <img src="Edit_5fc38f3d-2561-4189-87c2-197e3ff30b2e.png" alt="" /></span><span></span><span style="font-family:Verdana;"> and <img src="Edit_bfe99d90-7e55-4466-96b2-ce107483f69b.png" alt="" /></span><span></span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set <img src="Edit_543608fd-d8c9-4109-a285-bcf9377f43cc.png" alt="" /></span><span></span><span style="font-family:Verdana;">. Finally</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the numerical simulation has been done for showing the effectiveness of our analytical results.</span>展开更多
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
文摘In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (<img src="Edit_bced8210-1c24-4e78-bb5b-60ea7d37361c.png" alt="" /></span><span></span><span style="font-family:Verdana;">)</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> we reach the model disease-free equilibrium. Using Choquet integral</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Infected</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Recovered</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> susceptible-Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium <img src="Edit_cc2d122d-7c04-4fb7-a96a-3eb919a3785d.png" alt="" /> </span><span style="font-family:Verdana;">is globally asymptotically stable if <img src="Edit_0974e52f-cf63-4bfa-9781-1ebce366a4a3.png" alt="" /></span><span></span><span style="font-family:Verdana;"> or if the basic reproduction number is less than one (<img src="Edit_dbffcb03-cd00-4213-b7e1-ada9a0cf5c98.png" alt="" /></span><span></span><span style="font-family:Verdana;">). When <img src="Edit_5fc38f3d-2561-4189-87c2-197e3ff30b2e.png" alt="" /></span><span></span><span style="font-family:Verdana;"> and <img src="Edit_bfe99d90-7e55-4466-96b2-ce107483f69b.png" alt="" /></span><span></span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set <img src="Edit_543608fd-d8c9-4109-a285-bcf9377f43cc.png" alt="" /></span><span></span><span style="font-family:Verdana;">. Finally</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the numerical simulation has been done for showing the effectiveness of our analytical results.</span>
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.
