Human papillomavirus (HPV) is described in the source as the most common sexually transmitted infection; most sexually active individuals will be exposed and the majority of infections resolve spontaneously. Persistent infection with high-risk HPV types is, however, the leading cause of cervical cancer globally. Given this public-health context, the study investigated how awareness campaigns and vaccination influence HPV transmission dynamics by constructing and analysing a mathematical model enhanced by neural-network approximation.
The stated objective was to evaluate the impact of awareness interventions on HPV spread and to combine classical epidemiological analysis with machine-learning methods to validate and reproduce system dynamics numerically.
The authors developed a deterministic compartmental model for HPV transmission. Within the study they examined fundamental mathematical properties of the system including boundedness, the existence and characterization of disease-free and endemic equilibrium points, and derivation of the reproduction number as a threshold quantity for transmission.
These analytical steps establish the model framework needed to interpret whether control measures such as vaccination and awareness can move the system below the transmission threshold defined by the reproduction number.
For numerical work, the deterministic solution of the HPV transmission model was obtained using the ode45 solver based on the Runge–Kutta method. The time trajectories produced by this solver were then used as training data for a feedforward neural network which acted as a surrogate approximation model. The surrogate was intended to validate and reproduce the dynamical behaviour of the differential-equation model.
Evaluative metrics reported in the source abstract included mean square error, validation performance, gradient, and mu for the neural-network training and validation across different parameter scenarios.
Using the derived reproduction number, the authors investigated the stability of the disease-free and endemic equilibria. The reproduction number was treated as the key threshold parameter: its value determines whether an infection can invade and persist or die out in the population. The abstract indicates that stability analysis was performed in relation to this threshold quantity.
A sensitivity analysis was undertaken to identify which model parameter(s) most strongly affect HPV spread and control. The source confirms that sensitivity analysis was performed but does not provide, in the abstract, the names or ranks of the most sensitive parameter(s). Therefore specific sensitivity rankings and parameter values are not reported in this summary because they were not stated in the source abstract.
Numerical simulation experiments explored outcomes across varying levels of vaccination coverage, public awareness, and cervical infection rates. The simulations assessed neural-network training metrics (mean square error, validation performance, gradient, mu) while comparing model behaviour under the different public-health scenarios.
The principal finding reported in the abstract is that increased vaccination and higher levels of awareness about HPV risk play a crucial role in controlling spread of the virus in the population according to the model and surrogate simulations. The study therefore supports interventions combining vaccination and education campaigns as important for epidemic control.
Quantitative outcomes, such as specific reductions in prevalence, threshold vaccination coverage, or numerical sensitivity indices, were not included in the abstract and thus are not provided here.
The abstract documents the modeling approach, neural-network surrogate methodology, and qualitative simulation conclusions but does not report detailed numerical results, parameter estimates, or which specific parameter(s) were identified as most sensitive in the sensitivity analysis. It also does not report cohort or population-specific demographic assumptions, exact model compartmental structure, or specific vaccination scenarios (e.g., coverage levels or vaccine efficacy values) in the abstract. These details likely appear in the full article but are not available in the source abstract excerpt.
The source states the authors declared no competing interests. Citation details in the source: Kamil Shah et al., Sci Rep. 2026;16(1):24277. DOI: 10.1038/s41598-026-51555-2. The abstract lists the primary keywords as: HPV transmission; Neural networks; Numerical results; Stability analysis.
Note: All statements above are based on the information contained in the provided source abstract. Specific numeric results, parameter values, or full sensitivity rankings were not reported in that abstract and are therefore not included here.