Effects of insecticides and awareness on the dynamics of a delayed malaria model: A real-data calibration

We introduce a time-delayed human-malaria interaction model to examine the dynamics of malaria transmission and to evaluate the impact of awareness-based interventions. In this study, we incorporate two time delays: one representing the incubation period of malaria during transmission and the other accounting for the time required to organize and implement awareness programs. The delayed and non-delayed models are calibrated using observed malaria case data from India, the Democratic Republic of the Congo, and Uganda, and their predictive performance is assessed using relevant evaluation metrics to determine their accuracy and reliability. In the non-delayed model, variance-based MeFAST and correlation-based LHS-PRCC global sensitivity analyses are conducted to determine the key parameters that significantly influence the model dynamics. Based on the convergence test and statistical analyses, the two methods yield nearly the same number of significant parameters for the infected compartments. The existence of periodic oscillations emerging with a stable limit cycle is established by analyzing a supercritical Hopf bifurcation associated with the decay rate of awareness. Subsequently, in the delayed system, the direction and stability of the delay-induced Hopf bifurcation have been demonstrated using the normal form and the center manifold theorem, revealing the supercritical Hopf bifurcation and highlighting the challenges in controlling disease spread. Compared to a single delay, the presence of multiple delays destabilizes the system earlier and lowers the delay threshold for periodic behavior. Chaotic dynamics has been observed due to the high value of time delay in reported cases of infectives which reflects the importance of low delay value in awareness to control the spread of the disease. Despite chaotic behavior, the high availability of treatment and the extensive use of insecticides have been found to effectively control the dynamics.The delayed optimal control results indicate that the combination of insecticide measures and treatment is the most effective in controlling infections.