A new mathematical model has been developed to analyze the dynamics of sexually transmitted infectious diseases (STIDs), offering fresh insights for controlling these widespread infections. Published on January 31, 2025, this study employs sophisticated fractional order calculus to improve predictions of STID propagation, which have posed significant public health challenges worldwide.
The issue of STIDs is pressing, with the World Health Organization estimating 376 million new cases each year, leading to substantial health, social, and economic consequences. Researchers led by M. Rafique and colleagues from Majmaah University and Princess Nourah bint Abdulrahman University explored how existing models, often rooted in integer-order mathematics, fail to capture the complex nature of these diseases.
Traditional epidemic models typically utilize integer derivatives, which, according to the authors, "do not capture the nonlinear and complex dynamics" involved in the spread of STIDs. This oversight can lead to inadequate public health interventions as such models fail to account for the memory effects and delays inherent to disease transmission.
To address this gap, the researchers implemented fractional calculus along with time-delayed differential equations, creating what they describe as a time-delayed non-integer order STID model. This approach recognizes the significance of historical infection data, capturing the interplay between current infection rates and past transmission behaviors.
The study affirms the unique existence of solutions to this complex model, demonstrating its boundedness and non-negativity, which are pivotal for ensuring biological relevance within the predictions generated. The authors noted, "The fractional order system is complicated and hence there is no way to get exact analytical solutions."
Using the Grünwald-Letnikov method, the researchers performed numerical simulations to visualize the expected behaviors of STID dynamics. These simulations illuminate how modifying social behaviors—such as increasing condom use and improving access to health education—can dramatically influence infection rates. The authors assert, "The proposed fractional order delayed model can be used as a generalizable framework with which to pursue investigation of other infectious diseases and to develop interventions."
Key findings highlighted the model's ability to identify two equilibrium states: the disease-free state and endemic state, with the basic reproduction number ">R0" serving as a threshold indicator. When ">R0" exceeds 1, the authors predict persistent infection spread; conversely, values below 1 suggest containment of the disease.
By incorporating realistic delay factors, the model suggests effective strategies for reducing STID transmission. The authors concluded, "Stabilization and control of disease dynamics are highly sensitive to τ,” referring to the time-delay parameter, which plays a decisive role in infection management. This nuanced approach could serve not only for STIDs but also provide frameworks adaptable for modeling other infectious diseases.
The findings of this study indicate the necessity of revisiting traditional epidemic models to incorporate advanced mathematical concepts, ensuring public health policies are sufficiently equipped to handle the ever-evolving nature of infectious diseases.