A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics
To address the urgent need to accurately predict the spreading trend of the COVID-19 epidemic, a continuous Markov-chain model was, for the first time, developed in this work to predict the spread of COVID-19 infection. A probability matrix of infection was first developed in this model based upon t...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-01-01
|
| Series: | Biology |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2079-7737/11/2/190 |
| _version_ | 1797482591360647168 |
|---|---|
| author | Zhaobin Xu Hongmei Zhang Zuyi Huang |
| author_facet | Zhaobin Xu Hongmei Zhang Zuyi Huang |
| author_sort | Zhaobin Xu |
| collection | DOAJ |
| description | To address the urgent need to accurately predict the spreading trend of the COVID-19 epidemic, a continuous Markov-chain model was, for the first time, developed in this work to predict the spread of COVID-19 infection. A probability matrix of infection was first developed in this model based upon the contact frequency of individuals within the population, the individual’s characteristics, and other factors that can effectively reflect the epidemic’s temporal and spatial variation characteristics. The Markov-chain model was then extended to incorporate both the mutation effect of COVID-19 and the decaying effect of antibodies. The developed comprehensive Markov-chain model that integrates the aforementioned factors was finally tested by real data to predict the trend of the COVID-19 epidemic. The result shows that our model can effectively avoid the prediction dilemma that may exist with traditional ordinary differential equations model, such as the susceptible–infectious–recovered (SIR) model. Meanwhile, it can forecast the epidemic distribution and predict the epidemic hotspots geographically at different times. It is also demonstrated in our result that the influence of the population’s spatial and geographic distribution in a herd infection event is needed in the model for a better prediction of the epidemic trend. At the same time, our result indicates that no simple derivative relationship exists between the threshold of herd immunity and the virus basic reproduction number <i>R</i><sub>0</sub>. The threshold of herd immunity achieved through natural immunity is significantly higher than 1 − 1/<i>R</i><sub>0</sub>. These not only explain the theoretical misconceptions of herd immunity thresholds in herd immunity theory but also provide a guidance for predicting the optimal vaccination coverage. In addition, our model can predict the temporal and spatial distribution of infections in different epidemic waves. It is implied from our model that it is challenging to eradicate COVID-19 in the short term for a large population size and a wide spatial distribution. It is predicted that COVID-19 is likely to coexist with humans for a long time and that it will exhibit multipoint epidemic effects at a later stage. The statistical evidence is consistent with our prediction and strongly supports our modeling results. |
| first_indexed | 2024-03-09T22:35:33Z |
| format | Article |
| id | doaj.art-2e7643d24923428e9f886c256fb8ea85 |
| institution | Directory Open Access Journal |
| issn | 2079-7737 |
| language | English |
| last_indexed | 2024-03-09T22:35:33Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Biology |
| spelling | doaj.art-2e7643d24923428e9f886c256fb8ea852023-11-23T18:49:27ZengMDPI AGBiology2079-77372022-01-0111219010.3390/biology11020190A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic DynamicsZhaobin Xu0Hongmei Zhang1Zuyi Huang2Department of Life Science, Dezhou University, Dezhou 253023, ChinaDepartment of Life Science, Dezhou University, Dezhou 253023, ChinaDepartment of Chemical and Biological Engineering, Villanova University, Villanova, PA 19085, USATo address the urgent need to accurately predict the spreading trend of the COVID-19 epidemic, a continuous Markov-chain model was, for the first time, developed in this work to predict the spread of COVID-19 infection. A probability matrix of infection was first developed in this model based upon the contact frequency of individuals within the population, the individual’s characteristics, and other factors that can effectively reflect the epidemic’s temporal and spatial variation characteristics. The Markov-chain model was then extended to incorporate both the mutation effect of COVID-19 and the decaying effect of antibodies. The developed comprehensive Markov-chain model that integrates the aforementioned factors was finally tested by real data to predict the trend of the COVID-19 epidemic. The result shows that our model can effectively avoid the prediction dilemma that may exist with traditional ordinary differential equations model, such as the susceptible–infectious–recovered (SIR) model. Meanwhile, it can forecast the epidemic distribution and predict the epidemic hotspots geographically at different times. It is also demonstrated in our result that the influence of the population’s spatial and geographic distribution in a herd infection event is needed in the model for a better prediction of the epidemic trend. At the same time, our result indicates that no simple derivative relationship exists between the threshold of herd immunity and the virus basic reproduction number <i>R</i><sub>0</sub>. The threshold of herd immunity achieved through natural immunity is significantly higher than 1 − 1/<i>R</i><sub>0</sub>. These not only explain the theoretical misconceptions of herd immunity thresholds in herd immunity theory but also provide a guidance for predicting the optimal vaccination coverage. In addition, our model can predict the temporal and spatial distribution of infections in different epidemic waves. It is implied from our model that it is challenging to eradicate COVID-19 in the short term for a large population size and a wide spatial distribution. It is predicted that COVID-19 is likely to coexist with humans for a long time and that it will exhibit multipoint epidemic effects at a later stage. The statistical evidence is consistent with our prediction and strongly supports our modeling results.https://www.mdpi.com/2079-7737/11/2/190Markov-chain modelCOVID-19reproduction numbermutationherd immunity threshold |
| spellingShingle | Zhaobin Xu Hongmei Zhang Zuyi Huang A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics Biology Markov-chain model COVID-19 reproduction number mutation herd immunity threshold |
| title | A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics |
| title_full | A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics |
| title_fullStr | A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics |
| title_full_unstemmed | A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics |
| title_short | A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics |
| title_sort | continuous markov chain model for the simulation of covid 19 epidemic dynamics |
| topic | Markov-chain model COVID-19 reproduction number mutation herd immunity threshold |
| url | https://www.mdpi.com/2079-7737/11/2/190 |
| work_keys_str_mv | AT zhaobinxu acontinuousmarkovchainmodelforthesimulationofcovid19epidemicdynamics AT hongmeizhang acontinuousmarkovchainmodelforthesimulationofcovid19epidemicdynamics AT zuyihuang acontinuousmarkovchainmodelforthesimulationofcovid19epidemicdynamics AT zhaobinxu continuousmarkovchainmodelforthesimulationofcovid19epidemicdynamics AT hongmeizhang continuousmarkovchainmodelforthesimulationofcovid19epidemicdynamics AT zuyihuang continuousmarkovchainmodelforthesimulationofcovid19epidemicdynamics |