TY - JOUR

T1 - Mathematical and numerical model for the malaria transmission

T2 - Euler method scheme for a malarial model

AU - Ijaz Khan, M.

AU - Al-Khaled, Kamel

AU - Raza, Ali

AU - Khan, Sami Ullah

AU - Omar, Jiyan

AU - Galal, Ahmed M.

N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.

PY - 2022

Y1 - 2022

N2 - This research study has developed a mathematical model for malaria disease which is not only applicable for the case when the recovered humans return to the susceptible class, but also provides the directions for the case when the recovered humans also return to the infectious class. The model is simulated by using the Euler, Runge-Kutta-4 (RK-4), and nonstandard finite difference (NSFD) scheme. Firstly, the model is simulated by the Euler scheme and RK4 scheme and obtained graphical depiction for the endemic equilibrium as well as for the disease-free equilibrium (DFE). Then the mathematical model of malaria is simulated by an NSFD scheme and its graphical interpretation shows that it is suitable for all step sizes, i.e., it gives converging results even for very large step sizes. It is shown that the NSFD scheme is an unconditionally stable numerical scheme at a large step size. It is concluded that parameter R is greater than unity in the disease manifestation of the landlord population in the long term and when the parameter R is less than unity then the DFE is asymptotically stable.

AB - This research study has developed a mathematical model for malaria disease which is not only applicable for the case when the recovered humans return to the susceptible class, but also provides the directions for the case when the recovered humans also return to the infectious class. The model is simulated by using the Euler, Runge-Kutta-4 (RK-4), and nonstandard finite difference (NSFD) scheme. Firstly, the model is simulated by the Euler scheme and RK4 scheme and obtained graphical depiction for the endemic equilibrium as well as for the disease-free equilibrium (DFE). Then the mathematical model of malaria is simulated by an NSFD scheme and its graphical interpretation shows that it is suitable for all step sizes, i.e., it gives converging results even for very large step sizes. It is shown that the NSFD scheme is an unconditionally stable numerical scheme at a large step size. It is concluded that parameter R is greater than unity in the disease manifestation of the landlord population in the long term and when the parameter R is less than unity then the DFE is asymptotically stable.

KW - Euler method scheme for a malarial model

KW - Malaria mathematical model

KW - malaria transmission of relapse

KW - numerical solution of malaria model

UR - http://www.scopus.com/inward/record.url?scp=85143733358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85143733358&partnerID=8YFLogxK

U2 - 10.1142/S0217979223501588

DO - 10.1142/S0217979223501588

M3 - Article

AN - SCOPUS:85143733358

SN - 0217-9792

JO - International Journal of Modern Physics B

JF - International Journal of Modern Physics B

M1 - 2350158

ER -