# An Enhanced SEIR Model for Prediction of COVID-19 with Vaccination Effect

^{1}

^{2}

^{*}

## Abstract

**:**

_{0}is 1.3. Vaccination of infants and kids will be considered as future work.

## 1. Introduction

- To enhance SEIR Model with effect different versions of severity.
- To predict the susceptibility, infection and recovered using enhanced model with no social distancing is considered.
- To predict the susceptibility, infection and recovered using enhanced model with social distancing is considered.
- To predict the susceptibility, infection and recovered using enhanced model with social distancing with vaccination is considered.

## 2. Background

- N = total number of population of a geographical location, (S + I + R = N)
- β is the average number of contacts per person per time
- γ is the transition rate assumed to be proportional to the number of infectious individuals

## 3. Related Work

_{0}is produced. According to their findings, the pace at which vulnerable persons A are recruited significantly impacted the spread of infectious illnesses. As a result, even with vaccines, measures such as travel restrictions and public gathering bans should be implemented for an extended period to maintain the low recruitment rate of vulnerable persons A. This research might aid in the prediction and eradication of infectious illnesses.

_{0}was variable and uncontrolled in theory. Parameters such as vaccine effectiveness and vaccination rate may be tweaked alternatively.

#### Novelty of the Proposed Research Work

^{1}, I

^{2}, and I

^{3}. As such, the new model proposed was SEI (I

^{1}, I

^{2}, and I

^{3}) RV model. The I

^{1}, I

^{2}, and I

^{3}were individuals who suffer with mild infection who do not require hospitalization (I

^{1}), individuals with severe infection who require hospitalization (I

^{2}), and individuals with critical infection who require admittance to ICU (I

^{3}). The infection rates were represented as ${\beta}^{1}$, ${\beta}^{2}$, and ${\beta}^{3}$. The proposed model was derived for COVID-19 cases.

## 4. Proposed Method

^{1}), individuals with severe infection who require hospitalization (I

^{2}), individuals with critical infection who require admittance to ICU (I

^{3}), individuals who have recovered from the disease and have become immune (R), dead individuals (D), and vaccinated individuals (V). The design of the proposed model is shown in Figure 1. The proposed model has five major compartments viz. susceptible, exposed, infected, removed, and vaccination.

^{1}(where no severity and no hospitalization was required), I

^{2}(there was some severity and patients hospitalized), and the last sub compartment was infection I

^{3}(there was severity and patients were hospitalized in ICU). Similarly, the transmission rate was divided with ${\beta}^{1}$, ${\beta}^{2}$, and ${\beta}^{3}$.

_{0}= S + V + E + I

^{1}+ I

^{2}+ I

^{3}+ R + D

_{0}is Equations (15) and (16):

## 5. Result and Discussion

#### 5.1. Without Intervention of Social Distancing

#### 5.2. With Intervention of Social Distancing

_{0}as 1.3, and an epidemic growth rate of 0.01 per day. A significant decrease of 0.8619 was observed in the value of R

_{0}. Further, the doubling rate for the number of infected cases increased to 54.5 days.

#### 5.3. Impact of Social Distancing and Vaccination on the Number of Infectious Cases

## 6. Conclusions

_{0}is 2.1619. The proposed model is mathematically simulated and tested in different situations, such as without intervention of social distancing, and with the intervention of social distancing. The model predicted an epidemic growth rate of about 0.06 per day, and the number of infected people doubled after every 10.7 days. By imparting social distancing, the proposed model obtained the value of R

_{0}is 1.3. Finally, it can be inferred that social distancing norms and vaccination drive play a significant role in overcoming COVID-19. In the future, the proposed model will be enhanced by incorporating new compartments, such as vaccination of infants and kids, hospitalization, etc.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Proposed Model. Ψ—The rate at which individuals are vaccinated, γ—Rate at which infected individuals in class I

^{1}, I

^{2}and I

^{3}recovered from the disease and immunity is developed, β—Rate at which one infected in class I

^{1}, I

^{2}and I

^{3}contact susceptible and infect all of them. Thus, the susceptible individuals changed to exposed individuals, I

^{1}—Rate of mild infection and hospitalization.

**Figure 2.**Trends of number of people in different categories over a period of 365 days without social distancing and vaccination. Susceptible individuals (S), Exposed individuals (E), Individuals who have recovered from the disease and have become immune (R), Dead individuals (D), and Vaccinated individuals (V), Individuals suffer with mild infection who do not require hospitalization (I

^{1}), Individuals with severe infection who require hospitalization (I

^{2}), Individuals with critical infection who require admittance to ICU (I

^{3}).

**Figure 3.**Impact of Social Distancing on number of cases in various categories. Susceptible individuals (S), Exposed individuals (E), Individuals who have recovered from the disease and have become immune (R), Dead individuals (D), and Vaccinated individuals (V), Individuals suffer with mild infection who do not require hospitalization (I

^{1}), Individuals with severe infection who require hospi-talization (I

^{2}), Individuals with critical infection who require admittance to ICU (I

^{3}).

S. N. | Name of Company | Name of Vaccine |
---|---|---|

1 | Moderna | mRNA-1273 |

2 | Pfizer/BioNTech | BNT162b2 |

3 | Janssen (Johnson & Johnson) | Ad26.COV2.S |

4 | Oxford/AstraZeneca | AZD1222 |

5 | Serum Institute of India | Covishield |

6 | Bharat Biotech | Covaxin |

7 | Sinopharm (Beijing) | BBIBP-CorV (Vero Cells) |

8 | Sinovac | CoronaVac |

S. N. | Name of Country | % of Population Fully Vaccination |
---|---|---|

1 | India | 37.3% |

2 | United States | 60.8% |

3 | Brazil | 65.6% |

4 | Indonesia | 37.7% |

5 | Japan | 77.9% |

6 | Russia | 42.6% |

7 | Germany | 69.5% |

8 | United Kingdom | 69.5% |

9 | France | 71.0% |

10 | Iran | 57.3% |

11 | Saudi Arabia | 65.5% |

12 | Egypt | 16.4% |

13 | South Africa | 25.8% |

14 | United Arab Emirates | 91.1% |

15 | Nigeria | 1.9% |

S. N. | Acronym | Name of Model | Parameter Added | Definition |
---|---|---|---|---|

1 | SIS [7] | Susceptible-Infectious-Susceptible | Simplest form | Immunity does not build |

2 | SIRD [8] | Susceptible-Infectious-Recovered-Deceased | Deceased | D is the mortality rate |

3 | MSIR [9] | Maternal-Susceptible-Infectious-Recovered | Maternally Derived Immune | Newborn babies which are immune to a specific disease, such as measles |

4 | SICR [10] | Susceptible-Infectious-Carrier-Recovered | Carrier | It is applicable on those where infection resides in the body forever, such as TB |

5 | SUQC [11] | Susceptible-Unquarantined, Quarantine-Confirmed | Unquarantined, Quarantine | Number of people who are quarantined and unquarantined. |

6 | GSIR [12] | Generalized-Susceptible-Infectious-Recovered | Generalized | Assumed that throughout time, many waves of varied peak amplitude and form arise and fade away |

7 | SEIHR [13] | Generalized-Susceptible-Infectious-Hospitalized-Recovered | Hospitalized | Number of persons hospitalized |

8 | SCEIR [14] | Susceptible-Exposed-Infectious-Recovered-Removed | Confined | When an individual is experiencing lockdown |

9 | ISSEIR [15] | Interacting Subpopulation- Susceptible-Exposed-Infectious-Recovered | Interacting Subpopulation | Separate SEIR model between each subgroup of the population |

10 | SEIRV [16] | Susceptible-Infectious-Recovered-Vaccination | Vaccination | When the population is vaccinated |

Name of Coefficient | Definition |
---|---|

${N}_{0}$ | Total population (comprising 1000 individuals in this research) |

S | Susceptible individuals |

${\beta}^{1}$ | Rate at which one infected in class I^{1} contact susceptible and infect all of them. Thus, the susceptible individuals changed to exposed individuals. |

${\beta}^{2}$ | Rate at which one infected in class I^{2} contact susceptible and infect all of them. Thus, the susceptible individuals changed to exposed individuals. |

${\beta}^{3}$ | Rate at which one infected in class I^{3} contact susceptible and infect all of them. Thus, the susceptible individuals changed to exposed individuals. |

I^{1} | Rate of mild infection and hospitalization not required. |

I^{2} | Rate of severe infection and hospitalization is required. |

I^{3} | Rate of critical infection and I.C.U. is required. |

E | Set of exposed individuals; they are infected but not asymptotic and infectious. |

V | Set of vaccinated persons. |

${\gamma}^{1}$ | Rate at which infected individuals in class I^{1} recovered from the disease and immunity is developed. |

${\gamma}^{2}$ | Rate at which infected individuals in class I^{2} recovered from the disease and immunity is developed. |

${\gamma}^{3}$ | Rate at which infected individuals in class I^{3} recover from the disease and immunity is developed. |

p^{1} | Rate at which one infected in class I^{1} is shifted to class I^{2}_{.} |

p^{2} | Rate at which one infected in class I^{2} is shifted to class I^{3}_{.} |

R | Set of individuals who have recovered from the disease and are now immune. |

λ | Rate of natural (those who are not deceased from the COVID-19). |

$\mu $ | The death rate of individuals in the most severe stage of disease. |

Ψ | The rate at which individuals are vaccinated |

η | Vaccine inefficacy |

D | Set of removed populations |

Coefficient | Crude Birth Rate (σ) | λ | η | ψ |
---|---|---|---|---|

$\beta $ | 0.0 | 0.00025 | 0.0 | 0.0 |

α | 0.2 | - | - | - |

γ | 0.0 | 0.08 | 0.06818182 | 0.08571429 |

$p$ | 0.0 | 0.02 | 0.02272727 | - |

$\mu $ | 0.057142857 | - | - | - |

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**MDPI and ACS Style**

Poonia, R.C.; Saudagar, A.K.J.; Altameem, A.; Alkhathami, M.; Khan, M.B.; Hasanat, M.H.A. An Enhanced SEIR Model for Prediction of COVID-19 with Vaccination Effect. *Life* **2022**, *12*, 647.
https://doi.org/10.3390/life12050647

**AMA Style**

Poonia RC, Saudagar AKJ, Altameem A, Alkhathami M, Khan MB, Hasanat MHA. An Enhanced SEIR Model for Prediction of COVID-19 with Vaccination Effect. *Life*. 2022; 12(5):647.
https://doi.org/10.3390/life12050647

**Chicago/Turabian Style**

Poonia, Ramesh Chandra, Abdul Khader Jilani Saudagar, Abdullah Altameem, Mohammed Alkhathami, Muhammad Badruddin Khan, and Mozaherul Hoque Abul Hasanat. 2022. "An Enhanced SEIR Model for Prediction of COVID-19 with Vaccination Effect" *Life* 12, no. 5: 647.
https://doi.org/10.3390/life12050647