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The application of next generation matrix in the calculation of basic reproduction number for COVID-19
E Kalluci1, E Noka1, O Gordani1
1Department of Applied Mathematics, Faculty of Natural Sciences, University of Tirana.
Background:
Infectious diseases are disorders caused by microorganisms such as bacteria, viruses, fungi, or parasites. Many organisms live in and on our bodies. They are normally harmless or even helpful. However under certain conditions, some organisms may cause disease. Infectious diseases are also called contagious diseases due to the fact that they can be passed from person to person. Some are transmitted by insects or other animals. COVID-19 is an infectious disease that has "pervaded" the whole world during the last three years. The World Health Organization (WHO) has declared COVID-19 a Public Health Emergency of International Concern.
Methods:
In this paper, we will study the outbreak of this pandemic in Albania based on some mathematical models, such as SIR, SIRD, and SEIRD. We will present a detailed analysis of these models and also demonstrate how they can be used to predict the spread of infectious diseases. More precisely, we will see the spread of COVID-19 in our country, Albania. Software such as MATLAB and RStudio will be used to do this. The data that we will use when working with these programs is taken from the Institute of Public Health, Tirana, Albania.
Results:
We've developed an application utilizing actual data to estimate SEIRD model parameters. It's able to compute the basic reproduction number and, more significantly, provides forecasts on the disease's progression.
Conclusions:
Our aim is to calculate the Basic Reproduction Number, using the Next Generation Matrix, and use it to see the future of the disease. This is the average number of new infections generated by an infected individual. A large value indicates that the infection is transmitted very quickly. We will try to calculate what the values of Basic Number Reproduction have been over different time periods.
Insights
This study models COVID-19 spread in Albania using SEIRD, SIR, and SIRD mathematical models. Researchers calculated the basic reproduction number to predict future disease transmission dynamics.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- Infectious diseases, including COVID-19, pose significant global health challenges.
- COVID-19, a highly transmissible infectious disease, was declared a Public Health Emergency of International Concern by the WHO.
- Understanding disease transmission is crucial for effective public health interventions.
Purpose of the Study:
- To analyze the COVID-19 outbreak in Albania using mathematical modeling.
- To apply SIR, SIRD, and SEIRD models for predicting infectious disease spread.
- To estimate key epidemiological parameters and forecast disease progression.
Main Methods:
- Utilized mathematical models: SIR, SIRD, and SEIRD.
- Developed an application for parameter estimation using real-world data.
- Employed MATLAB and RStudio for data analysis and modeling.
Main Results:
- Successfully estimated SEIRD model parameters from actual data.
- Computed the basic reproduction number (R0).
- Generated forecasts for disease progression.
Conclusions:
- The basic reproduction number was calculated using the Next Generation Matrix.
- Analysis of R0 over time provides insights into transmission dynamics.
- Mathematical modeling offers a valuable tool for understanding and predicting infectious disease outbreaks.
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