A novel ABC fractional-order mathematical model for malaria transmission dynamics incorporating treatment-seeking behavior

Malaria remains a significant global health challenge, particularly in developing countries. This study introduces a novel ABC fractional-order model to analyze malaria transmission dynamics, incorporating treatment-seeking behavior, which includes both treatment at professional health facilities and interventions through indigenous traditional medicine. We conducted a comprehensive analysis of the model, examining the existence and uniqueness of solutions and performing numerical simulations using various mathematical techniques. Our findings reveal that fractional-order effects significantly influence malaria transmission dynamics; specifically, higher fractional orders result in slower increases in susceptible and exposed human populations while leading to more rapid changes in the dynamics of infected populations. Furthermore, the model demonstrates that increasing the rate of treatment at health facilities can substantially reduce the infected population and decrease the reproduction number, thereby facilitating the elimination of the disease within a shorter time frame. Additionally, the study highlights that reliance on traditional medicine without clinical validation may lead to temporary recovery but not complete elimination of the malaria parasite, increasing the risk of relapse and further disease spread. The finding suggests that public health initiatives should encourage collaboration between traditional medicine practitioners and professional healthcare providers to reduce non-standardized treatment risks and improve the effectiveness of malaria management strategies. These contribute to the broader field of epidemiological modeling, offering a robust framework for understanding and mitigating malaria transmission in resource-limited settings.