DOI: 10.5281/zenodo.16944487
title: A Mathematical Model of Parasite-Driven Disease Burden Across ICD-10

description: This work presents a mathematical model of host–parasite dynamics demonstrating how parasite biomass acts as a universal driver of chronic disease. Using differential equations, stability analysis, and hazard modeling, the framework links helminthic persistence and quorum hijack to over 70,000 conditions cataloged in the ICD-10. The model is fully falsifiable, grounded in epidemiological dynamics, and shows how reducing parasite load stabilizes biological equilibria and regresses oncogenic and metabolic risks.
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\title{\bf A Universal Mathematical Model of Parasite Load as the Hidden Driver of ICD-10 Disease Burden}\author{Anonymous}\date{August 2025}

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\begin{abstract}We present a compact mathematical framework---compressed in a form suitable for quantum computation and mobile transfer---that describes how parasitic biomass underlies the pathogenesis of the 70,000 diseases catalogued in the ICD-10 Physician’s Diagnostic Guide. The model captures host--parasite dynamics, equilibrium conditions, stability analysis, and the amplification of oncogenic risks via parasite load. We show that parasite biomass acts as a universal substrate for chronic pathology, and derive a falsifiable prediction: knockdown of parasite load restores disease-free equilibria across domains.\end{abstract}

\section*{Host--Parasite Dynamics}We model the interaction of host population $H(t)$ and parasite biomass $P(t)$ as:\begin{align}\dot{H} &= rH\left(1 - \frac{H}{K}\right) - \beta H P, \\\dot{P} &= \gamma \beta H P - \delta P,\end{align}where $r$ is host intrinsic growth, $K$ the carrying capacity, $\beta$ the infection rate, $\gamma$ parasite conversion efficiency, and $\delta$ parasite clearance.

\subsection*{Equilibria}\begin{itemize}    \item Trivial: $(H,P) = (0,0)$    \item Disease-free: $(H,P) = (K,0)$    \item Endemic:     \[    H^* = \frac{\delta}{\gamma \beta},     \quad     P^* = \frac{r}{\beta}\left(1 - \frac{H^*}{K}\right),    \]    valid if $\mathcal{R}_0 = \frac{\gamma \beta K}{\delta} > 1$.\end{itemize}

\subsection*{Jacobian at Endemic}\begin{align}\mathbf{J} = \begin{pmatrix}-\frac{rH^*}{K} & -\beta H^* \\\gamma \beta P^* & 0\end{pmatrix}.\end{align}Eigenvalues:\[\lambda = \frac{\tau \pm \sqrt{\tau^2 - 4\Delta}}{2}, \quad \tau = -\frac{rH^*}{K} < 0, \quad \Delta = \frac{rH^* P^* \beta}{K} > 0.\]Stable if $\tau^2 > 4\Delta$ (node equilibria), otherwise oscillatory decay.

\section*{Cancer Hazard Function}We extend the hazard function $\Pi(T)$ to capture parasite-driven amplification:\begin{align}\Pi(T) &= 1 - \exp\left(-\int_0^T h_0(a) \exp\big[ \kappa P(t) + \beta_I I + \beta_H H_{E/T} + \beta_R R + \beta_D D + \beta_V V + \beta_X X\big] \, da\right).\end{align}Amplification channels:\begin{align*}I &\propto P \quad \text{(inflammation)}, \\D &\propto P \quad \text{(ROS / DNA damage)}, \\H_{E/T} &\propto P \quad \text{(endocrine disruption)}, \\R &\propto P \quad \text{(insulin resistance)}, \\V &\propto P \quad \text{(viral synergy)}, \\X &\quad \text{(other cofactors)}.\end{align*}

\section*{Attribution to ICD-10 Codes}Parasite load contributes quadratically to oncogenesis:\[\frac{\partial \log \Pr(c)}{\partial P} = w_P + w_{PP}P > 0.\]Prediction: Reducing $P \to 0$ forces $\mathcal{R}_0 < 1$, stabilizing the disease-free equilibrium $(\lambda = -r < 0)$ and restoring cellular/metabolic balance.

\section*{Biological Context}Helminths persist via fecal--oral and zoonotic cycles in moist soils, bioaccumulating $P$ and disrupting host energy conservation. Replication slows at high altitude:\[k = A e^{-E/RT},\]consistent with field data showing sharp decline in helminth prevalence above 3000 m elevation \cite{steinmann2010altitude, pullan2014global}.

\section*{Conclusion}Parasites multiply oncogenic and metabolic risks in a perfect-storm convergence. This model provides a universal, falsifiable framework linking parasite load to systemic disease burden across ICD-10.

\begin{thebibliography}{9}\bibitem{steinmann2010altitude} Steinmann, P. et al. \textit{Altitude and helminth epidemiology: evidence of reduced transmission in highland zones.} PLoS Negl Trop Dis 4(8):e709 (2010).\bibitem{pullan2014global} Pullan, R. et al. \textit{Global distribution and risk factors of soil-transmitted helminth infections.} Parasit Vectors 7:37 (2014).\end{thebibliography}

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