Numerical method for the solution of a malaria model using the collocation method
DOI:
https://doi.org/10.65221/0168Keywords:
collocation method, approximate solution, Hermite polynomial and power series polynomial, Malaria modelAbstract
This work proposes an approximate solution to a malaria transmission model based on power series expansions and the Hermite collocation method. The work presents the malaria dynamics as a system of nonlinear differential equations that describe the susceptible and infected populations among humans and vectors. The model equations are turned into a set of solvable terms using power series techniques, which allows for analytical insight into the solution structure. The Hermite collocation approach is then used as a numerical approximation tool, employing orthogonal basis functions to generate very precise and stable solutions, even for complicated nonlinearities in the malaria model. Numerical simulations employing this integrated technique show convergence and high agreement between the approximate solutions for various parameters. The findings demonstrate the historical evolution of susceptible and infected classes, offering important epidemiological insights into disease progression and control. This hybrid analytical-numerical framework provides an effective and computationally efficient tool for investigating malaria transmission patterns, allowing for more accurate design of public health interventions and vector control tactics.
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