🦠 microbiology

Modeling the Impact of Dynamic Gastric pH on Helicobacter pylori Eradication and Antibiotic Resistance Emergence

This paper presents an extended mathematical model incorporating dynamic gastric pH fluctuations driven by bacterial urease activity, host acid secretion, and dietary factors to analyze how pH-dependent reproductive thresholds influence *H. pylori* eradication success and the emergence of antibiotic resistance, thereby offering a theoretical framework for optimizing treatment strategies through pH modulation.

Original authors: KOUSSOK, A. H. S., Onyango, E. R., Fujimoto, K., Tewa, J. J.

Published 2026-02-26

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: KOUSSOK, A. H. S., Onyango, E. R., Fujimoto, K., Tewa, J. J.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine your stomach is a fortress. Inside this fortress lives a tiny, stubborn invader called Helicobacter pylori (or H. pylori). This bacterium is notorious for causing ulcers and even stomach cancer. For years, doctors have tried to kick it out using a "magic bullet" strategy: a cocktail of strong antibiotics. But here's the problem: the bacteria are getting smarter. They are evolving resistance, and the "magic bullets" are becoming less effective.

This paper is like a new, high-tech simulation game that helps scientists understand why the treatment sometimes fails and how to fix it. The authors realized that previous models missed one crucial variable: the pH level (acidity) of the stomach, and how it changes in real-time.

Here is the story of the paper, broken down into simple concepts and analogies.

1. The Stomach: A Shifting Battlefield

Think of your stomach acid as a moat filled with boiling lava. It's supposed to be too hot for anyone to survive.

The Bacteria's Trick: H. pylori has a special tool called urease. Imagine this as a "fire extinguisher." When the bacteria release urease, it neutralizes the acid, turning the boiling lava into a warm, safe pool where the bacteria can hide and multiply.
The Body's Defense: Your body is the castle guard. When it sees the bacteria turning down the heat, the guard tries to pump more acid back in to restore the lava moat.
The Diet Factor: Every time you eat, it's like throwing a bucket of water into the moat, temporarily cooling it down.

The Old Models: Previous computer models treated the stomach acid as a static, unchanging wall. They assumed the acid was always the same.
The New Model: This paper says, "Wait! The acid level is actually a dynamic variable that goes up and down like a seesaw, influenced by the bacteria, the body, and your lunch."

2. The Two Armies: Sensitive vs. Resistant

Inside the stomach, there are two types of bacterial armies:

The Sensitive Soldiers: These are the "normal" bacteria that die easily when antibiotics are introduced.
The Resistant Soldiers: These are the "super-bugs" that have learned to survive the antibiotics.

The goal of the treatment is to wipe out both armies. If you kill the sensitive ones but leave the resistant ones, the resistant ones take over the whole fortress.

3. The "Goldilocks" Zone of pH

The authors discovered that the acidity level (pH) acts like a thermostat that controls the success of the war.

Too Acidic (pH < 4.7): The lava is so hot that no bacteria can grow, even the resistant ones. This is a "kill zone" for the bacteria, but it's hard for antibiotics to work well here because some drugs break down in extreme acid.
Too Neutral (pH > 6.0): The bacteria are happy. They grow fast, and they can easily hide from the immune system.
The Sweet Spot (pH 5.0 – 6.0): This is the Therapeutic Window. In this zone, the bacteria are stressed (they don't grow well), but the antibiotics are at their peak power.

The Analogy: Imagine trying to catch a fish.

If the water is too cold (too acidic), the fish freezes and stops moving, but your net (antibiotic) is frozen too and doesn't work.
If the water is too warm (too neutral), the fish swims away too fast for your net.
You need the water to be just right so the fish is sluggish, but your net is working perfectly.

4. The Four Possible Outcomes

The researchers ran simulations to see what happens under different conditions. They found four distinct "endings" to the story:

Ending A: Total Victory (Eradication)
- What happens: The doctors manage to keep the stomach pH in the "Sweet Spot." The antibiotics kill the sensitive bacteria, and the immune system finishes off the resistant ones. The bacteria are gone, and the stomach returns to normal.
- Real life: This is the ideal cure.
Ending B: The Resistant Takeover (Treatment Failure)
- What happens: The antibiotics kill the weak bacteria, but the strong, resistant ones survive. Because they are still there, they keep pumping out their "fire extinguisher" (urease), raising the pH. This makes the stomach environment perfect for them but terrible for the remaining antibiotics. The resistant bacteria take over the whole stomach.
- Real life: This is why some people get sick again after treatment.
Ending C: The Stalemate (Coexistence)
- What happens: The bacteria and the immune system get into a weird balance. The bacteria aren't strong enough to win completely, but the immune system can't wipe them out. They live together in a chronic, low-level infection.
- Real life: This might explain why some people have long-term, low-grade stomach issues that never fully go away.
Ending D: The Rollercoaster (Oscillations)
- What happens: The system gets stuck in a loop. The bacteria grow, the immune system attacks, the pH changes, the bacteria hide, the immune system relaxes, and the bacteria grow again. It's a cycle of "flare-ups" and "remission."
- Real life: This could explain why some patients feel sick, then better, then sick again, even while taking medicine.

5. The Big Takeaway: Control the pH!

The most exciting part of this paper is the suggestion that we can manipulate the pH to win the war.

The authors propose a Two-Phase Strategy:

During Treatment: Use acid-suppressing drugs (like PPIs) to raise the pH just enough to hit that "Sweet Spot" (5.0–6.0). This makes the antibiotics super effective against the bacteria.
If Treatment Fails: If resistant bacteria survive, the strategy flips. Instead of raising the pH, you might want to keep the stomach very acidic (below 4.7). Why? Because at that extreme level, even the "super-bugs" can't grow, effectively starving them out.

Summary

This paper is a breakthrough because it stops treating the stomach as a static container and starts treating it as a living, breathing ecosystem where the acidity changes every minute.

By understanding that the bacteria, the body, and the food we eat are all constantly fighting over the pH level, doctors might be able to design smarter treatments. Instead of just throwing more antibiotics at the problem, they can tune the stomach's acidity to make the antibiotics work better and prevent the bacteria from hiding. It's like changing the rules of the game so the bacteria can't win, no matter how strong they get.

1. Problem Statement

Helicobacter pylori ($H. pylori$) is a major cause of gastric cancer and peptic ulcers, yet eradication rates remain low (20–40%) due to rising antibiotic resistance. Existing within-host mathematical models of $H. pylori$ infection typically treat the gastric environment as a static acidic barrier. However, they neglect the dynamic regulation of gastric pH, which is actively manipulated by:

Bacterial Urease: Neutralizes acid to create a protective niche.
Host Physiology: Acid secretion attempts to restore baseline acidity.
Dietary Perturbations: Meals cause transient pH fluctuations.

Since bacterial growth rates and antibiotic efficacy are highly pH-dependent, ignoring this dynamic variable limits the predictive power of current models regarding treatment failure and resistance emergence.

2. Methodology

The authors extended a previously published within-host model (Noguera et al.) by explicitly incorporating gastric pH ( $H(t)$ ) as a dynamic state variable coupled with bacterial populations and immune response.

A. Model Formulation

The system is described by a set of non-linear ordinary differential equations (ODEs) tracking:

$S(t)$ : Antibiotic-sensitive bacterial density.
$R(t)$ : Antibiotic-resistant bacterial density.
$T(t)$ : Immune response (T-lymphocytes).
$D_i(t)$ : Concentrations of three antibiotics (Clarithromycin, Rifampicin, Ciprofloxacin).
$H(t)$ : Gastric pH (the novel dynamic variable).

Key Mechanisms:

pH Dynamics (Eq. 1e): Modeled as a balance between bacterial urease activity (alkalinizing toward $H_{max} \approx 7$ ), host acid secretion (restoring baseline $H_0 \approx 2.5$ ), and dietary inputs (exponential decay).
pH-Dependent Growth: Bacterial growth rates ( $\beta_S, \beta_R$ ) follow a hyperbolic tangent function, peaking near neutral pH ( $H_{opt} = 7.0$ ).
pH-Dependent Antibiotic Efficacy: Killing rates ( $\kappa_i$ ) follow a Gaussian distribution, peaking in moderately acidic conditions ( $H_{opt,abx} = 5.5$ ), reflecting the stability of antibiotics under Proton Pump Inhibitor (PPI) therapy.
Resistance Mechanisms: Includes mutation from sensitive to resistant strains and horizontal gene transfer.

B. Analytical Approach

Non-dimensionalization: The system was scaled to reduce parameters and identify dimensionless groups.
Equilibrium Analysis: The authors derived all biologically feasible equilibria:
- Infection-Free Equilibrium (IFE).
- Resistant-only equilibria (with and without immune response).
- Coexistence equilibria (with and without immune response).
Reproductive Numbers: Defined pH-dependent basic reproductive numbers, $R_s(H)$ and $R_r(H)$ , representing the average number of new bacteria produced by a single bacterium at a specific pH.
Stability Analysis: Used Jacobian matrices and eigenvalue analysis (Routh-Hurwitz criteria) to determine local asymptotic stability of equilibria.

C. Numerical Simulations

Simulations were performed using a fourth-order Runge-Kutta method in Python to explore four clinical scenarios based on parameter variations (growth rates, antibiotic efficacy, carrying capacity).

3. Key Contributions

Dynamic pH Integration: This is the first within-host model to mechanistically couple bacterial urease activity, host acid secretion, and dietary inputs with antibiotic therapy dynamics.
pH-Dependent Thresholds: The derivation of $R_s(H)$ and $R_r(H)$ provides explicit, pH-dependent thresholds that dictate whether eradication, resistance dominance, or coexistence occurs.
Identification of "Therapeutic Windows": The model identifies specific pH ranges where both sensitive and resistant strains can be eradicated simultaneously, distinct from the optimal growth pH.
Dynamical Regimes: The study reveals that pH coupling fundamentally alters system dynamics, specifically by damping oscillations and confining them to the resistant-immune loop, contrasting with previous models that predicted sustained oscillations.

4. Results

The study identified four distinct dynamical regimes corresponding to clinical outcomes:

Scenario	Condition	Outcome	Dynamics
1. Successful Eradication	$R_s(H) < 1$ and $R_r(H) < 1$	Complete clearance of bacteria.	Rapid decline of both strains; pH returns to baseline ( $H_0$ ).
2. Resistant Persistence	$R_s(H) < 1$ but $R_r(H) > 1$	Sensitive strain cleared; resistant strain dominates.	Resistant bacteria maintain elevated pH, compromising antibiotic efficacy.
3. Stable Coexistence	$R_s(H) > 1$ , $R_r(H) > 1$ , and immune thresholds met.	Chronic polymicrobial infection.	Both strains persist under immune surveillance; pH remains near neutrality.
4. Oscillatory Dynamics	High carrying capacity + pH feedback.	Relapsing-remitting symptoms.	Damped oscillations with a ~15-day period, confined to resistant bacteria and immune response.

Key Findings from Simulations:

The "Acid Trap": Extremely low pH ( $< 4.7$ ) suppresses bacterial growth even for resistant strains, suggesting a potential post-treatment strategy.
The "Therapeutic Window": A narrow pH range (approx. 5.0–6.0) exists where antibiotic efficacy is maximized while bacterial growth is suboptimal, allowing for simultaneous eradication of both strains.
Oscillation Damping: The inclusion of pH feedback reduces the amplitude of oscillations compared to models without pH dynamics, suggesting that pH regulation acts as a stabilizing buffer against uncontrolled proliferation.

5. Significance and Clinical Implications

Rationale for Acid Suppression: The model mathematically justifies the use of Proton Pump Inhibitors (PPIs) in eradication therapy. PPIs shift gastric pH from the bacterial growth optimum (7.0) toward the antibiotic efficacy optimum (5.5), helping to drive $R_s$ and $R_r$ below unity.
Dietary Modulation Strategy: The authors propose a novel two-phase strategy:
1. During Treatment: Elevate pH to the therapeutic window (5.0–6.0) to maximize antibiotic killing.
2. Post-Failure/Prevention: Maintain highly acidic conditions (pH < 4.7) to suppress any surviving resistant strains that might otherwise thrive in neutralized environments.
Resistance Management: The model highlights that incomplete eradication allows resistant strains to elevate pH, creating a self-protective niche that further reduces drug efficacy. This underscores the need for aggressive, combination therapies to prevent the initial survival of resistant mutants.
Future Directions: The framework suggests that personalized pH monitoring and dietary interventions could be used to optimize treatment schedules, particularly in resource-limited settings or for multidrug-resistant cases.

In conclusion, this paper establishes gastric pH not merely as a background condition but as a central, dynamic control parameter in the host-pathogen-therapy triad, offering a refined theoretical basis for improving $H. pylori$ eradication strategies.