Some qualitative properties of the discrete models for malaria propagation

Faragó, István and Mosleh, R. (2023) Some qualitative properties of the discrete models for malaria propagation. APPLIED MATHEMATICS AND COMPUTATION, 439. No. 127628. ISSN 0096-3003

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Abstract

This paper addresses a reliable mathematical modeling of malaria propagation in infected societies for humans and mosquitoes with an extension of the basic Ross–Macdonald model. We analyze the extended Ross model numerically which is an initial value prob- lem of a seven-dimensional system of the first-order ODEs. For this aim, the discretized scheme of the extended model is split into two parts. First, we apply the step-size func- tions to approximate the time derivatives with the first-order consistency. Then we use a nonlocal discretization of the standard θ -method to the right side of the system to obtain a linear system. We find the conditions for the step-size functions under which specific intervals are positively invariant for the total populations and each component of the so- lution of the extended Ross model. We suggest a step-size function for the extended Ross model to preserve the dynamical consistency of the model for any step size �t. The nu- merical simulations confirm the theoretical results for the examples and we compare the efficiency of the nonstandard Runge–Kutta methods with the different step-size functions for sufficiently large step sizes.

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