PerTexP: scenario-based exploration of pertussis dynamics under maternal and infant vaccination

PerTexP is an interactive, stage-structured compartmental modeling tool designed to support evidence-based decision-making by enabling researchers and public health practitioners to explore and compare the impact of various maternal, infant, and booster vaccination strategies on pertussis transmission dynamics, with a specific focus on the Italian epidemiological context.

The Gist

Imagine a bustling city where a mischievous, invisible ghost named Pertussis (also known as Whooping Cough) is trying to sneak around and make people sick. While this ghost is scary for everyone, it is absolutely terrifying for the city's tiniest residents: babies. Babies are too small to fight back effectively, and if the ghost gets them, it can be very dangerous.

The city (Italy) has been trying to stop the ghost using two main shields:

1. The Mom's Shield: Giving pregnant moms a vaccine so they pass a temporary "force field" to their babies before they are even born.
2. The City's Shield: Giving vaccines to babies, children, and adults to keep the ghost from spreading.

But here's the problem: The ghost is tricky. Sometimes the shields wear off, and sometimes the ghost hides in people who don't even know they are sick (like teenagers or adults with a mild cough). The city leaders need to know: Which shield works best? Should we focus on the moms, or should we try to get more adults to get booster shots?

Enter PerTexP: The "Crystal Ball" Simulator

This paper introduces a new digital tool called PerTexP. Think of it as a high-tech flight simulator for public health.

Instead of guessing what will happen, researchers built a virtual version of the city inside a computer. This virtual city has two main neighborhoods:

• The Nursery: Where the babies (0–11 months) live.
• The Big World: Where everyone else (1 year and older) lives.

In this simulator, the researchers can tweak the "knobs" to see what happens. They can ask questions like:

• "What if we get 10% more moms vaccinated?"
• "What if we give 10% more adults their booster shots?"
• "What happens if the ghost gets a little luckier and spreads faster?"

How the Simulator Works (The Simple Version)

The tool uses a set of rules (math) to track how the ghost moves from person to person. It counts:

• The Vulnerable: People who can catch the ghost.
• The Protected: People with a shield (vaccine or mom's antibodies).
• The Infected: People currently carrying the ghost.
• The Recovered: People who fought it off (but might lose their immunity later).

The simulator runs the clock forward five years at a time, showing a "movie" of how many people get sick in each neighborhood under different scenarios.

What the Simulator Discovered

When the researchers ran the simulation using real data from Italy in 2024, they found some surprising and very helpful insights:

1. The "Mom's Shield" is the Heavy Lifter
When they increased the number of pregnant moms getting vaccinated, the number of sick babies dropped dramatically (by about 37%). It was like putting a giant, thick wall around the Nursery. Because the moms were protected, the ghost couldn't jump from the "Big World" into the "Nursery."

2. The "Adult Booster" is a Support Player
When they increased the number of adults getting booster shots, the number of sick babies only dropped a tiny bit (about 1%). However, it did help reduce the total number of sick people in the "Big World."

• Analogy: Think of the adult boosters as cleaning up the trash in the streets. It makes the whole city cleaner and safer, but it doesn't stop a specific intruder from breaking into the Nursery as effectively as the Mom's Shield does.

3. You Need Both to Win
The simulator showed that you can't just rely on one strategy. Even if you vaccinate every single mom, the ghost can still find a way to spread if the "Big World" is full of people with worn-out shields. To truly stop the ghost (reach a point where the disease dies out), you need both a strong Mom's Shield and a well-maintained City Shield.

Why This Matters

Before tools like PerTexP, health officials had to guess which strategy would work best, often waiting years to see the results in real life. PerTexP allows them to run thousands of "what-if" scenarios in minutes.

• For the Policymaker: It's like having a map that shows the safest route through a minefield. It tells them, "If you spend your budget here, you save the most babies."
• For the Public: It provides a clear, transparent way to understand why certain vaccination rules exist.

The Bottom Line

The paper concludes that while adult boosters are important for general health, vaccinating pregnant women is the single most effective way to protect the most vulnerable babies. The PerTexP tool is now available for other researchers and health officials to use, helping them navigate the complex world of disease control with a little more confidence and a lot less guessing.

In short: Protect the moms, protect the babies, and keep the whole city safe.

Technical Summary

1. Problem Statement

Despite high vaccination coverage in high-income countries, pertussis (whooping cough) continues to resurge, characterized by recurrent outbreaks and increased incidence among adolescents and adults. This re-emergence poses a critical threat to neonates and infants, who suffer the highest morbidity and mortality rates. Current control strategies rely heavily on childhood vaccination, but waning immunity and heterogeneous vaccine uptake across age groups complicate eradication efforts.

There is a lack of accessible, mathematically rigorous tools that allow public health practitioners to rapidly explore and compare different vaccination strategies (specifically maternal immunization, infant primary vaccination, and non-infant boosters) within a specific epidemiological context. The authors aim to fill this gap by developing PerTexP (Pertussis Time Exploration), a tool designed to support evidence-informed decision-making, particularly for the Italian epidemiological context.

2. Methodology

Mathematical Model

PerTexP is built upon a discrete-time, stage-structured compartmental model with a weekly time step ($t$). The population is divided into two age classes:

• Infants ($i=1$): Aged 0–11 months.
• Non-infants ($i=2$): Aged 1 year and older.

Within each age group, the model uses a SIR (Susceptible-Infected-Recovered) structure extended to include a vaccinated compartment ($V$).

• Compartments: $S_i$ (Susceptible), $V_i$ (Vaccinated/Protected), $I_i$ (Infected), $R_i$ (Recovered).
• Demographics: The model includes constant recruitment ($\Lambda$), natural mortality ($\mu_i$), disease-induced mortality ($d$, specific to infants), and ageing (transition from infants to non-infants with probability $\eta$).
• Vaccination Strategies:
  • Maternal: A fraction $p$ of newborns enters $V_1$ via maternal antibodies.
  • Infant Primary: Susceptible infants move to $V_1$ with probability $\psi_1$ (representing the DTaP series).
  • Boosters: Non-infants move to $V_2$ with probability $\psi_2$ (Tdap booster).
• Immunity Waning: Vaccine-induced immunity wanes in non-infants ($V_2 \to S_2$) with probability $\omega$. Natural immunity also wanes ($R_2 \to S_2$) with probability $\nu$.
• Transmission: Modeled via frequency-dependent transmission. The force of infection $\lambda_i$ depends on a contact matrix $C$ and the prevalence of infection in both age groups. The infection probability is $G_i(\lambda_i) = 1 - e^{-\lambda_i}$.

Reproduction Numbers

The authors derive the Control Reproduction Number ($R_c$) using the Next-Generation Matrix (NGM) approach adapted for discrete-time systems. $R_c$ serves as the epidemic threshold; if $R_c < 1$, the disease is expected to die out. The basic reproduction number ($R_0$) is derived as a special case where vaccination parameters are zero.

Parametrization and Implementation

• Context: The model is parametrized using 2024 Italian demographic statistics (ISTAT) and clinical data.
• Time Horizon: 5 years (260 weeks).
• Software: Implemented as a MATLAB App with a Graphical User Interface (GUI).
• Stochasticity: To assess robustness, the authors introduce random perturbations (multiplicative noise) to state variables at yearly intervals, simulating unobserved factors.

3. Key Contributions

1. Development of PerTexP: Creation of an interactive, user-friendly MATLAB tool that allows non-programmers to simulate pertussis dynamics under various vaccination scenarios.
2. Discrete-Time Framework: Adoption of a discrete-time model suitable for short-term projections and weekly reporting intervals, balancing biological complexity with parameter identifiability.
3. Integrated Vaccination Modeling: Explicit incorporation of three distinct strategies: maternal immunization, infant primary vaccination, and non-infant booster uptake, including their specific waning rates and effectiveness factors.
4. Quantitative Sensitivity Analysis: Systematic evaluation of how variations in maternal coverage ($p$), infant coverage ($\psi_1$), and booster coverage ($\psi_2$) impact $R_c$ and cumulative incidence.

4. Results

Baseline Projections (2024 Italian Scenario)

• Under current 2024 parameters, the model projects an increasing trend in pertussis incidence over five years.
• Total cumulative cases rise from ~612 in Year 1 to ~4,871 in Year 5.
• Infants account for only ~5% of total cases but represent the highest risk group for severe outcomes.
• The baseline Control Reproduction Number is $R_c \approx 1.037$, indicating sustained transmission.

Impact of Vaccination Strategies

• Sensitivity to Maternal Immunization: $R_c$ is highly sensitive to maternal coverage ($p$). However, even at high levels, maternal vaccination alone cannot drive $R_c$ below 1.
• Sensitivity to Boosters: $R_c$ is less sensitive to booster coverage ($\psi_2$) at high levels, showing diminishing returns.
• Comparative Intervention Analysis:
  • Increasing maternal coverage by 10% (from 62.6% to 68.9%) resulted in a 37.85% reduction in cumulative infant cases and a 29.7% reduction in non-infant cases over five years.
  • Increasing booster coverage by 10% resulted in only a ~1.2% reduction in cumulative cases for both groups.
• Conclusion: Boosters primarily reduce incidence in non-infants and act as a supporting strategy, whereas increasing maternal immunization is the most effective lever for reducing the burden on the most vulnerable infant population.

Robustness

• Introducing random perturbations (5% noise) confirmed that the qualitative behavior of the deterministic model remains stable, though annual fluctuations can occur.

5. Significance

• Public Health Decision Support: PerTexP provides a transparent, accessible platform for health officials to visualize the trade-offs between different vaccination policies.
• Strategic Insight: The study confirms that while booster programs are necessary for herd immunity in older populations, maternal immunization is the critical intervention for protecting infants, who are most at risk of mortality.
• Policy Alignment: The findings align with recent recommendations from the European Centre for Disease Prevention and Control (ECDC), reinforcing the need for combined strategies rather than relying on a single intervention.
• Scalability: While currently parametrized for Italy, the underlying model structure is generalizable to other regions, provided local demographic and transmission data are available.

The paper concludes that PerTexP is a valuable resource for exploring "what-if" scenarios, offering a rigorous yet practical approach to optimizing pertussis control strategies in the face of waning immunity and heterogeneous vaccine uptake.