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Abstract
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Malaria disease, which is of parasitic origin, has always been one of the challenges for
human societies in areas with poor sanitation. The lack of proper distribution of drugs and lack of
awareness of people in such environments cause us to see many deaths every year, especially in children
under the age of five. Due to the importance of this issue, in this paper, a new five-compartmental
(c1, c2)-fractal-fractional SIR-SI-model of malaria disease for humans and mosquitoes is presented.
We use the generalized Mittag-Leffler fractal-fractional derivatives to design such a mathematical
model. In different ways, we study all theoretical aspects of solutions such as the existence, uniqueness
and stability. A Newton polynomial that works in fractal-fractional settings is shown, which allows us
to get some numerical trajectories. From the trajectories, we saw that an increase in antimalarial
treatment in consideration to memory effects reduces the peak of sick individuals, and mosquito
insecticide spraying minimizes the disease burden in all compartments.
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