Data-driven modeling of imported malaria in Morocco and the impact of population migration.

Malaria remains a very critical health-threatening issue worldwide, and increasingly, migration is viewed as a cause of re-emergence in malaria-free zones. This study proposes a data-driven, deterministic compartmental model that explicitly accounts for human immigration when modeling malaria transmission from humans to mosquito populations. The human host is categorized into susceptible, asymptomatic, infected, and recovered classes, while the vector population is stratified into susceptible and infected compartments. The paper presents a rigorous mathematical analysis to prove the positivity and uniqueness of solutions, and further demonstrates that the model only admits a globally stable endemic equilibrium. Using Morocco as a case study, key parameters are estimated using three complementary methods: least-squares fit, Extended Kalman Filter, and Long Short-Term Memory (LSTM) neural networks, which where applied to imported malaria data from 1990 through 2023. To identify the best control measures to prevent the possible re-establishment of malaria in Morocco, we investigate an optimal control problem that includes awareness, prophylactic treatment, treatment of the infected population, and vector control with insecticide. The goal is to identify the optimal effectiveness of these controls. Numerical results show a significant reduction in human and vector infections through a combination of control strategies, thus underscoring the importance of surveillance and control policies that account for migration. Therfore, it serves as a practical, flexible framework to analyze imported malaria and other vector-borne diseases across similarly high-mobility areas.