Abstract
In this paper, we used the modified
G
′
G
2
-expansion method and unified method to examine the novel complex solutions to the malaria model utilising the conformable derivative, which is an important biological concept. For the with-host malaria model, it is utilised to simulate the dynamics of malaria infection. To assess the efficiency of various control measures utilise the malaria model, they can aid in the identification of treatments in high-risk areas by assisting public health experts. We obtained several solutions using trigonometric, hyperbolic and rational solutions. The investigation of modulation instability to the malaria model was also indicated. Additionally, using the appropriate parameters, the physical behaviour of some of the results obtained is displayed as 3-D, 2-D and contour graphs. All of the provided results were verified using the software Mathematica by reinserting them into the malaria model. These findings demonstrate that the methods we have stated are easy to apply effective, exact and that they may be used to a wide range of additional challenging issues. The results are new, fascinating and helpful to better understand the dispersion mechanisms and energy transmission in modelling of a number of interesting disciplines including biomedical sciences. Comparing the results to those from the literature, earlier studies reveal that they are unique and distinctive. Our discoveries also represent the physical phenomena and layout of novel complex solutions. Actually, the governing model’s wave performances are defined by these solutions. We believe that this research is timely and that a wide range of professionals who work on physicists, biological and engineering models will be interested in it.