Mathematical Modeling of Soil-Transmitted Helminth Infection: Human-Animal Dynamics with Environmental Reservoirs

TL;DR

This study examines the dynamics of STH transmission using a deterministic compartmental model and nonlinear ordinary differential equations and derived the basic reproduction number and demonstrated that the disease-free and endemic equilibrium points are asymptotically stable under specific thresholds.

Abstract

Soil-transmitted helminth (STH) infections, one of the most prevalent neglected tropical diseases, pose a significant threat to public health in tropical and subtropical areas. These parasites infect humans and animals through direct contact with contaminated soil or accidental ingestion. This study examines the dynamics of STH transmission using a deterministic compartmental model and nonlinear ordinary differential equations. Our model incorporates the roles humans, animals, and the environment play as reservoirs for spreading STH. We derived the basic reproduction number and demonstrate that the disease-free and endemic equilibrium points are asymptotically stable under specific thresholds. We also performed a sensitivity analysis to determine how each parameter affects the model's output. The sensitivity analysis identifies key parameters influencing infection rates, such as ingestion rate, disease progression rate, and shedding rate, all of which increase infection. Conversely, higher clearance and recovery rates decrease infection. The study also highlights the potential for cross-species transmission of STH infections between humans and animals, underscoring the One Health concept, which acknowledges the interdependence of human, animal, and environmental health.

Figures (6)

• Figure 1: Compartmental diagram for the helminth model. The dashed lines indicate the interaction of the human and animal populations with the contaminated environment that leads to the ingestion of parasitic eggs. The dotted dashed lines indicate the release of eggs by individuals or animals infected with parasitic helminths, leading to environmental contamination.
• Figure 2: Local sensitivity analysis of model parameters to $R_0$. (a) Parameters associated with the human and parasitic egg population (b) Parameters associated with the animal population. Positive values (e.g., $\beta_a$, $\varepsilon_a$) suggest that increasing these parameters raises $R_0$, while negative values (e.g., $\mu_m$, $\gamma_a$, $b_a$) indicate that increasing these parameters reduces $R_0$ subsequently leading to a decrease in the infection.
• Figure 3: PRCC values depicting the sensitivity of the model's output over time for (a) Infected humans (b) Infected animals and (c) Parasitic egg population to the model parameters. Higher PRCC values signify a stronger correlation between a parameter and the population analyzed. The ingestion rates $\beta_a,\beta_h$, shedding rates $\varepsilon_a,\varepsilon_h$, and progression rates $\rho_a,\rho_h$ exhibit positive PRCC values whilst the recovery rates $\gamma_a, \gamma_h$ and clearance rate $\mu_m$ show negative PRCC values.
• Figure 4: Profile distribution of the human population (a) Susceptible, (b) Exposed, and (c) Infected for varying initial parasitic egg populations in the contaminated environment $m_0$. A rapid decline in the susceptible population and an increase in the exposed and infected populations are observed. As $m_0$ increases, the decline in the susceptible population occurs over a longer period, and fewer individuals are exposed.
• Figure 5: Profile distribution of the animal population (a) Susceptible, (b) Exposed, and (c) Infected for varying initial parasitic egg populations in the contaminated environment $m_0$. The susceptible population declines rapidly, while the exposed and infected populations increase. As $m_0$, decreases, the decline in the susceptible population takes longer and fewer individuals are exposed. A similar trend is observed in the infected animal population as $m_0$ decreases.

Theorems & Definitions (5)

• Theorem 1
• proof
• Theorem 2
• Theorem 3
• Definition 1