A multi-scale mathematical framework for modelling the dynamic nature of autism spectrum disorder symptoms:...

Autism Spectrum Disorder (ASD) is characterised by persistent deficits in social communication and interaction alongside restricted, repetitive patterns of behaviour, interests, or activities. Standard diagnostic criteria provide static descriptions, failing to capture the dynamic variability of these symptoms across contexts and developmental trajectories. Furthermore, current descriptions often lack mechanistic explanations for why these symptom fluctuations occur. There is a need for dynamic, theory-driven models that bridge neurobiological mechanisms with observable clinical phenomena.

This study aimed to develop and present a set of interpretable mathematical models representing the dynamic, context-dependent nature of the core symptoms of ASD, explicitly grounded in established neuropsychological theories including Predictive Coding, Information Theory, and Network Neuroscience principles.

Mathematical models were theoretically derived using algebraic and differential equations to represent hypothetical symptom dynamics across both diagnostic domains. Social reciprocity was modelled using modulated exponential decay functions derived from executive function and predictive processing theories. Nonverbal communication was represented by weighted summation reflecting multi-channel integration demands. Relationship development was modelled using sigmoid growth functions incorporating social motivation theory. Stereotyped movements were represented by sinusoidal functions conceptualised as homeostatic entropy-reduction mechanisms. Insistence on sameness was modelled using sigmoid preference functions explicitly derived from Bayesian precision-weighting of prediction errors. Restricted interests were represented by exponential functions reflecting atypical reward processing. Sensory sensitivities were modelled using integral functions representing habituation failure due to excitation-inhibition imbalance. No empirical data were collected; parameter ranges were derived from theoretical considerations and existing literature.

The study produced theoretical mathematical equations that quantify the temporal dynamics and contextual modulation for each core symptom domain. These equations provide a formalised representation grounded in mechanistic principles: how social reciprocity would decay due to executive and predictive processing load, how nonverbal communication effectiveness would depend on multi-channel integration capacity, how relationships would develop under constraints of social motivation, how repetitive behaviours would fluctuate to regulate environmental entropy, how preference for sameness would emerge from aberrant Bayesian precision, how restricted interests would persist due to heightened reward salience, and how sensory sensitivities would accumulate due to habituation failure. These models generate testable quantitative predictions about symptom patterns and intervention effects.

The proposed mathematical models offer a novel, quantitative framework for understanding and representing the dynamic nature of ASD symptoms. By integrating mechanistic neurobiological theories with dynamic mathematical formulations, these interpretable models provide a potential advance over static descriptions and may facilitate improved clinical assessment, identification of intervention targets at the parameter level, personalised treatment strategies, and targeted research into the mechanisms underlying ASD. The framework respects neurodiversity by conceptualising many symptoms as adaptive responses to neurobiological differences rather than mere deficits. Empirical validation is required to test model predictions, estimate actual parameter values from clinical populations, and establish clinical utility.