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
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>
