SOLUTION TO MATHEMATICAL MODEL ON MALARIA TRANSMISSION DYNAMICS USING HOMOTOPY PERTURBATION METHOD (HPM)
Agada David Ojochogwu1*, Omale David1, Nurudeen Raimi2 &Abimbola Olanrewaju Michael3
1Department of Mathematical Science, Kogi State University, Anyigba, Nigeria
2Department of Physics, Kogi State University, Anyigba, Nigeria
3Department of Mathematics Education, University of Lagos, Nigeria
*Email: agadadavido2@gmail.com
ABSTRACT
Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years, with the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio- economic conditions. In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems both linear and non-linear. In this work, we used the Homotopy Perturbation Method (HPM) to obtain the analytic solution of the differential equations of the (SIR-SI) mathematical model and we apply the Bellman and Cooke’s theorem of stability to verify the stability of the model at equilibrium state. This work confirms the power, simplicity and efficacy of the method, also this method is a suitable method for solving any partial differential equations or system of partial differential equations as well.
| Definition of Variables S = Susceptible human I = Infected human R = Recovered human/Removed human Iv = Infected vector π= human birth rate λ= vector birth rate = Contact rate =Natural death rate = Death rate due to disease = Transmission rate between susceptible vector and infected human ω = Transmission rate between susceptible vector and infected human |
