# Deterministic modelling of asymptomatic spread and disease stage progression in vaccine preventable infectious diseases

## TL;DR

This paper presents a model to track how vaccine-preventable diseases spread silently and progress through different stages, using a diphtheria outbreak in Yemen as an example.

## Contribution

The study introduces a deterministic model for asymptomatic spread and disease progression in vaccine-preventable diseases.

## Key findings

- The basic reproduction number increases with higher transmission rates.
- The basic reproduction number decreases with higher vaccination rates.

## Abstract

This study introduces a deterministic formulation for modelling the asymptotic spread of a vaccine preventable disease as well as the different stages for the progression of the disease. We derive the formula for the associated basic reproduction number. To illustrate the proposed model, we use data from the 2017–2018 diphtheria outbreak in Yemen and fit the parameters of the model. A sensitivity analysis of the basic reproduction number, with respect to the model parameters, show that this number increases with an increase of the transmission rate while this number decreases when vaccination rate increases.