Frictional Order Host-Vector Model for Transmission of Dengue Fever
Rashid Jan1, Asif Jan2
1Rashid Jan, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an710049, PR China.
2Asif Jan, Department of Microbiology, Abasyn University, Peshawar 25000, KPK, Pakistan.
Manuscript received on January 27, 2017. | Revised Manuscript received on January 29, 2017. | Manuscript published on February 15, 2017. | PP: 12-15 | Volume-2 Issue-9, February 2017. | Retrieval Number: I0142022917
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Main purpose of this paper is to formulate an epidemiological model for dengue fever transmission using fractional order derivatives. Due to memory effect property, fractional order derivative has a benefit over the classical integer order models. This model for transmission of dengue fever of the non-integer order initial value problem will be based on the well-known fractional order Caputo derivative. Here our focus is on the existence of non-negative solutions of the frictional order dengue fever transmission model, furthermore, equilibria of the model and local asymptotic stability of model equilibria is investigated. In the end fractional order transmission model for dengue fever without immunity is presented.
Keywords: Dengue fever, Caputo derivative, Existence of positive solution, Model equilibria, Asymptotic stability.