Deterministic and ANN-based modelling of measles transmission using real epidemiological data.

This study aims to develop a nonlinear SVLIQR epidemic model to investigate measles transmission dynamics by incorporating vaccination, latency, quarantine, and treatment effects. The qualitative properties of the model, including positivity and boundedness of solutions, are established. The basic reproduction number is derived using the next-generation matrix method, and the existence of disease-free and endemic equilibrium points is examined. The local stability of the disease-free equilibrium is analysed using the Routh-Hurwitz criterion, while global stability is studied through the Castillo-Chávez approach. In addition, model parameters are estimated using the least squares method based on reported measles cases in China from 2005 to 2017. To improve the numerical approximation and capture the nonlinear dynamics of the system, an ANN-based solver coupled with the ode45 scheme is implemented. The results show that the model fits the reported data well, and the ANN framework provides highly accurate and convergent approximations under different epidemiological parameter settings. Numerical simulations further indicate that higher vaccination and quarantine rates significantly reduce measles transmission. Overall, the proposed framework provides a useful and reliable tool for understanding measles dynamics and assessing effective intervention strategies.