TY - JOUR
T1 - Fractional model of HIV transmission with awareness effect
AU - Fatmawati,
AU - Khan, Muhammad Altaf
AU - Odinsyah, Hafidz Putra
N1 - Funding Information:
The authors are thankful to the anonymous reviewers for their careful reading and suggestions that improved the presentation of the paper greatly. This work was supported by Universitas Airlangga through Hibah Riset Mandat (No. 342/UN3.14/LT/2019 ).
Publisher Copyright:
© 2020
PY - 2020/9
Y1 - 2020/9
N2 - In this work, we study the HIV dynamics with fractional operator of Caputo type. We use the real data of HIV infection cases of Indonesia from 2006 to 2018 and parameterized the HIV model and estimate the basic reproduction number is R0≈2.2763. First, we give brief mathematical formulation of HIV/AIDS population in integer order derivative. Then, we present some background results related to the model. The integer model is then generalized by using the Caputo derivative and present the mathematical results that associated to the model. We use novel technique for the solution of fractional mathematical model of HIV using Newton polynomial approach and obtain the numerical solution graphically. The data fitting versus model for fractional order p is shown which shows that the model give better result than the integer order. Some graphical for the important parameter were shown. The model is shown locally asymptotically when R0 less or greater than 1.
AB - In this work, we study the HIV dynamics with fractional operator of Caputo type. We use the real data of HIV infection cases of Indonesia from 2006 to 2018 and parameterized the HIV model and estimate the basic reproduction number is R0≈2.2763. First, we give brief mathematical formulation of HIV/AIDS population in integer order derivative. Then, we present some background results related to the model. The integer model is then generalized by using the Caputo derivative and present the mathematical results that associated to the model. We use novel technique for the solution of fractional mathematical model of HIV using Newton polynomial approach and obtain the numerical solution graphically. The data fitting versus model for fractional order p is shown which shows that the model give better result than the integer order. Some graphical for the important parameter were shown. The model is shown locally asymptotically when R0 less or greater than 1.
KW - Caputo derivative
KW - HIV cases
KW - HIV model
KW - Parameter estimations
UR - http://www.scopus.com/inward/record.url?scp=85086464663&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2020.109967
DO - 10.1016/j.chaos.2020.109967
M3 - Article
AN - SCOPUS:85086464663
SN - 0960-0779
VL - 138
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 109967
ER -
