Monkeypox Transmission Dynamics Using Fractional Disease Informed Neural Network: A Global and Continental Analysis

The global outbreak of Monkeypox has emerged as a significant concern in recent years, as per the World Health Organization (WHO). It is essential to study the transmission dynamics of the disease to project its progression and design future mitigation strategies. Models and projections provide evidence for rapid policy decisions and timely interventions. The proposed study attempts to address two significant existing limitations. First, classical models of monkeypox exhibit an inability to capture epidemiological patterns associated with global and regional data. Second, research on the transmission dynamics of Monkeypox in areas such as Asia, North America, South America, Antarctica, and globally is needed. This study aims to fill these gaps by hybridizing the power of fractional calculus and Neural Networks (NN) to develop a more unified understanding of disease dynamics, enabling effective strategies for controlling and mitigating Monkeypox transmission. The study also investigates and compares monkeypox transmission dynamics across all six continents and globally, using a comprehensive WHO dataset. The model was trained using 1053 days of data points from January 5, 2022, to March 18, 2025, and was subsequently used to obtain future predictions of Monkeypox transmission dynamics across all studied regions. The results show that in fractional Disease-Informed Neural Networks (DINN), the memory effect and nonlocality associated with the disease transmission were captured using the Caputo Fractional derivative to understand and mitigate Monkeypox transmission. The study utilised data from the world, as well as from Africa, Asia, Oceania, Europe, North America, and South America, to estimate disease and fractional-order parameters for various regions using the trained DINN. Notable findings include that the progression rate of the disease from exposure to infectious humans $({\beta })$ is relatively high in Oceania (0.1558) and Asia (0.1497), whereas Africa (0.0703) has the lowest value. The clinically ill rate $({\gamma })$ is highest in Asia (0.2694), followed by South America (0.2503) and Europe (0.2438), with the lowest value observed in Africa (0.1225). The contact rate between infected rodents and susceptible humans $({{\eta }_{2}})$ is highest in Asia. For fractional-order parameters, $q_{6}$ consistently has very high values across all regions, indicating low memory effect and nonlocality. These findings underscore the critical role of DINN, using fractional-order compartmental models, in studying and controlling Monkeypox disease globally and in various regions. Notably, this hybrid model is computationally expensive; thus, further research on addressing this limitation could be a future scope.