Measles is a highly contagious infectious disease caused by a virus in the paramyxovirus family. Mathematical models for epidemics are useful tools for understanding and predicting epidemic spread and its dynamics. These mathematical models allow researchers to simulate the spread of measles in the population by presenting the interactions between susceptible, exposed, infected, recovered, and vaccinated individuals. In this paper, an improved SEIRV+D model is developed based on known epidemiology models such as the SIR and SEIR models. The interactions between different compartments are given as a system of six Ordinary Differential Equations (ODEs) that represent the dynamics of the model. Additionally, the natural death rate and natural birth rate are considered. One of the key issues in epidemiology models is the reproduction number, which indicates the average number of secondary infections caused by a single infected individual. Another key issue is the disease-free equilibrium point (steady state) that can help predict disease outbreaks. Both the basic reproduction number and the disease-free equilibrium point have been obtained for the developed model. A case study for North Macedonia is analyzed for two different vaccination rates to demonstrate the impact of vaccination.
Epidemic Model, Measles, SEIRV+D Model
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