Stochastic Modelling of Early-Life Stress and Long-Term Psychological Well-Being: Thresholds in a Shot-Noise Model of Allostatic Load

References

[1] Felitti VJ, Anda RF, Nordenberg D, Williamson DF, Spitz AM, Edwards V, et al. Relationship of childhood abuse and household dysfunction to many of the leading causes of death in adults: The Adverse Childhood Experiences (ACE) Study. American Journal of Preventive Medicine. 1998;14(4):245–258.

[2] Hughes K, Bellis MA, Hardcastle KA, Sethi D, Butchart A, Mikton C, et al. The effect of multiple adverse childhood experiences on health: a systematic review and meta-analysis. The Lancet Public Health. 2017;2(8):e356–e366.

[3] McEwen BS, Stellar E. Stress and the individual: mechanisms leading to disease. Archives of Internal Medicine. 1993;153(18):2093–2101.

[4] Sterling P, Eyer J. Allostasis: a new paradigm to explain arousal pathology. In: Fisher S, Reason JT, editors. Handbook of life stress, cognition and health. Chichester (UK): Wiley; 1988. p. 629–649.

[5] Hertzman C. The biological embedding of early experience and its effects on health in adulthood. Annals of the New York Academy of Sciences. 1999;896(1):85–95.

[6] Miller GE, Chen E, Parker KJ. Psychological stress in childhood and susceptibility to the chronic diseases of aging: moving toward a model of behavioral and biological mechanisms. Psychological Bulletin. 2011;137(6):959–997.

[7] Heim C, Mletzko T, Purselle D, Musselman DL, Nemeroff CB. The dexamethasone/corticotropin-releasing factor test in men with major depression: role of childhood trauma. Biological Psychiatry. 2008;63:398–405.

[8] Newport DJ, Heim C, Bonsall R, Miller AH, Nemeroff CB. Pituitary-adrenal responses to standard and low-dose dexamethasone suppression tests in adult survivors of child abuse. Biological Psychiatry. 2004;55(1):10–20.

[9] Bunea I, Szentágotai-Tătar A, Miu AC. Early-life adversity and cortisol response to social stress: a meta-analysis. Translational Psychiatry. 2017;7:1274.

[10] Marques-Feixa L, Palma-Gudiel H, Romero S, et al. Childhood maltreatment disrupts HPA-axis activity under basal and stress conditions in a dose–response relationship in children and adolescents. Psychological Medicine. 2023;53(3):1060–1073.

[11] Perrone L, Thorpe D, Shariat Panahi G, Kitagawa Y, Lindhiem O, Bernard K. Meta-analysis of associations between childhood adversity and diurnal cortisol regulation. Development and Psychopathology. 2024;36:1323–1355.

[12] Benthem de Grave R, Hasselman F, Bijleveld E. From work stress to disease: A computational model. PLoS ONE. 2022;17(2):e0263966.

[13] Rao R, Androulakis IP. Allostatic adaptation and personalized physiological trade-offs in the circadian regulation of the HPA axis: A mathematical modeling approach. Scientific Reports. 2019;9:11212.

[14] van de Leemput IA, Wichers M, Cramer AOJ, et al. Critical slowing down as early warning for the onset and termination of depression. Proceedings of the National Academy of Sciences. 2014;111(1):87–92.

[15] Bondesson L. Shot-noise distributions. In: Generalized gamma convolutions and related classes of distributions and densities. Lecture Notes in Statistics 76. New York: Springer; 1992. ch. 10, p. 152–159.

[16] Iksanov AM, Jurek ZJ. Shot noise distributions and selfdecomposability. Stochastic Analysis and Applications. 2003;21(3):593–609.

[17] Barndorff-Nielsen OE, Shephard N. Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society: Series B. 2001;63(2):167–241.

[18] Anda RF, Porter LE, Brown DW. Inside the adverse childhood experience score: strengths, limitations, and misapplications. American Journal of Preventive Medicine. 2020;59(2):293–295.

[19] Meehan AJ, Baldwin JR, Lewis SJ, MacLeod JG, Danese A. Poor individual risk classification from adverse childhood experiences screening. American Journal of Preventive Medicine. 2021. https://doi.org/10.1016/j.amepre.2021.08.008

[20] Waugh CE, Sali AW. Resilience as the ability to maintain well-being: An allostatic active inference model. Journal of Intelligence. 2023;11(8):158.

@article{1724899,
      author = {Andanje Mulambula},
      title = {Stochastic Modelling of Early-Life Stress and Long-Term Psychological Well-Being: Thresholds in a Shot-Noise Model of Allostatic Load},
      journal = {Iconic Research And Engineering Journals},
      year = {2026},
      volume = {10},
      number = {5},
      pages = {1656-1673},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1724899.pdf},
      abstract = {Early-life stress is reliably associated with poorer psychological well-being decades later, but the mechanism by which an exposure that ends in childhood continues to act in adulthood is not settled. This paper formalises the question as a problem in stochastic processes. Allostatic load is modelled as a shot-noise process driven by a Poisson stream of stressors with exponentially distributed magnitudes and a homeostatic recovery rate. Two results follow. First, in the constant-parameter model the influence of a childhood stressor on adult load decays exponentially and is numerically extinct within a decade, so the state variable cannot carry the observed persistence; persistence must instead enter through a parameter. Second, when childhood exposure is allowed to lower the recovery rate, the stationary load distribution is exactly Gamma with shape equal to the ratio of the stressor arrival rate to the recovery rate, and two exposure thresholds appear in closed form. At the first, the modal load leaves zero and the typical state changes from recovered to elevated. At the second, located by a digamma equation, the rate of threshold crossings is maximised; beyond it episodes become fewer but longer, so disturbance shifts from episodic to chronic. The exceedance probability, episode rate and mean episode duration all have closed forms, each confirmed against exact simulation. The model further predicts that exposures of equal count but earlier timing carry greater adult risk, a prediction count-based epidemiology cannot test.},
      keywords = {Allostatic load; biological embedding; early-life stress; shot-noise process; stationary distribution; threshold behaviour},
      month = {November},
      doi = {https://doi.org/10.64388/ire1724899}
  }