# A Two-Dose Vaccine Epidemic Model with Power Incidence Rate

## TL;DR

This paper introduces a novel epidemic model incorporating a two-dose vaccine with power-law incidence rates, analyzing its steady states and the effects of different parameters through numerical simulations.

## Contribution

It develops a new SIVR model with power incidence rates and examines the impact of vaccine doses and parameters on disease dynamics.

## Key findings

- Steady state conditions for disease-free and endemic equilibria are derived.
- Numerical simulations show how parameters $(p;q)$ influence infection levels.
- The model highlights the importance of second-dose vaccination in controlling epidemics.

## Abstract

The dynamics of a SIVR model with power relationship incidence rates $(\beta I^p S^q)$ is investigated. It is assumed an individual can be susceptible after receiving the first dose of the vaccine, hence a second dose is required to attain permanent immunity. The steady states conditions of the disease-free equilibrium and the endemic equilibrium are critically presented. Numerical simulations are carried out to determine the impact of the exponential parameters $(p;q)$ on infection.