Complex travelling wave solutions of fractional nonlinear coupled malaria model: bifurcation, chaos, and multistability.

This study explore the dynamics of malaria transmission utilizing a novel fractional nonlinear coupled malaria model with a beta derivative, intending to expand our understanding of the complex factors that drive disease spread. By using the General Exponential Rational Function Method (GERFM), the fractional nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, yielding a range of complex traveling wave solutions, including kink, anti-kink, and dark solitons. The physical behavior of these attained solutions is illustrated through detailed 2D and 3D graphs. The analysis shows key outcomes such as the occurrence of bifurcation analysis, quasi-periodic and chaotic patterns, as well as multi-stability and sensitivity within the model, underscoring the elaborate nature of malaria transmission dynamics. These findings offer new understanding into the modeling of disease spread and provide a strong structure for future research in malaria control. Finally, the study contributes to the development of more accurate predictive models with potential applications in the biomedical sciences, extending the role of fractional calculus in comprehension complex biological systems.