TY - JOUR

T1 - Fractional mathematical modeling of malaria disease with treatment & insecticides

AU - Sinan, Muhammad

AU - Ahmad, Hijaz

AU - Ahmad, Zubair

AU - Baili, Jamel

AU - Murtaza, Saqib

AU - Aiyashi, M. A.

AU - Botmart, Thongchai

N1 - Funding Information:
The Authors extend their thanks to the Deanship of Scientific Research at King Khalid University, Saudi Arabia for funding this work through the small research groups under grant number RGP. 1/387/42 .
Publisher Copyright:
© 2022

PY - 2022/3

Y1 - 2022/3

N2 - Many fatal diseases spread through vertical transmission while some of them spread through horizontal transmission and others transmit through both modes of transmission. Horizontal transmission illnesses are usually carried by a vector, which might be an animal, a bird, or an insect. Plasmodium parasites that dwell in red blood cells produce malaria, an infectious illness. This parasite is mostly transmitted to humans via mosquitoes. The dynamics of Malaria illness among human persons and vectors are examined in this study. The impact of the vector (mosquito) on disease transmission is also taken into account. The problem is described using nonlinear ODEs that are then generalized using the Atangana–Baleanu fractional derivative. Some theoretical analyses such as existence and uniqueness and stability via Ulam–Hyres stability analysis and optimal control strategies have been done. The numerical solution has been achieved via a numerical technique by implementing MATLAB software. Results of fractional, as well as classical order, are portrayed through different graphs while some figures are displayed for the global asymptotical stability of the model. From the graphical results, it can be noticed that the control parameters drastically decrease the number of infected human and vector population which will off course minimize the spread of infection among the human population. In addition to that, from the graphical results, it also be noticed that our model is globally asymptomatically stable as the solution converges to its equilibrium. Moreover, the use of bednets and insecticides can reduce the spread of infection dramatically while the impact of medication and treatment on the control of infection is comparatively less.

AB - Many fatal diseases spread through vertical transmission while some of them spread through horizontal transmission and others transmit through both modes of transmission. Horizontal transmission illnesses are usually carried by a vector, which might be an animal, a bird, or an insect. Plasmodium parasites that dwell in red blood cells produce malaria, an infectious illness. This parasite is mostly transmitted to humans via mosquitoes. The dynamics of Malaria illness among human persons and vectors are examined in this study. The impact of the vector (mosquito) on disease transmission is also taken into account. The problem is described using nonlinear ODEs that are then generalized using the Atangana–Baleanu fractional derivative. Some theoretical analyses such as existence and uniqueness and stability via Ulam–Hyres stability analysis and optimal control strategies have been done. The numerical solution has been achieved via a numerical technique by implementing MATLAB software. Results of fractional, as well as classical order, are portrayed through different graphs while some figures are displayed for the global asymptotical stability of the model. From the graphical results, it can be noticed that the control parameters drastically decrease the number of infected human and vector population which will off course minimize the spread of infection among the human population. In addition to that, from the graphical results, it also be noticed that our model is globally asymptomatically stable as the solution converges to its equilibrium. Moreover, the use of bednets and insecticides can reduce the spread of infection dramatically while the impact of medication and treatment on the control of infection is comparatively less.

KW - Atangana baleanu operator

KW - Existence and uniqueness

KW - Mathematical modeling

KW - Mittag-Leffler function

KW - Optimal control strategies

KW - Ulam stability analysis

UR - http://www.scopus.com/inward/record.url?scp=85123625379&partnerID=8YFLogxK

U2 - 10.1016/j.rinp.2022.105220

DO - 10.1016/j.rinp.2022.105220

M3 - Article

AN - SCOPUS:85123625379

SN - 2211-3797

VL - 34

JO - Results in Physics

JF - Results in Physics

M1 - 105220

ER -