# Impact of Infective Immigrants on COVID-19 Dynamics

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## Abstract

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## 1. Introduction

## 2. The Model

## 3. Model Analysis

## 4. Numerical Simulations

#### 4.1. Base Scenarios with Lower Transmissibility of the SARS-CoV-2

#### 4.2. Scenario with Higher Transmissibility of the SARS-CoV-2

#### 4.3. Further Sensitivity Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

COVID-19 | Coronavirus disease of 2019 |

## References

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**Figure 2.**Graphical representation of the sensitivity of the reproduction number ${R}_{0}$ using Latin hypercube sampling and the Partial rank correlation coefficients with 10,000 samples.

**Figure 3.**Contour plot of the basic reproduction number ${R}_{0}$ for different values of the effective contact rate $\beta $ and the vaccination rate v.

**Figure 4.**Contour plot of the basic reproduction number ${R}_{0}$ for different values of the vaccination rate v and waning immunity rate w.

**Figure 5.**Dynamics of the model sub-populations without inflow of infective immigrants and without vaccination.

**Figure 6.**Dynamics of the model sub-populations without inflow of infective immigrants and with vaccination.

**Figure 7.**Dynamics of several sub-populations with inflow of infective immigrants and without vaccination.

**Figure 8.**Dynamics of several sub-populations with inflow of infective immigrants and with vaccination.

**Figure 9.**Number of deaths, cumulative infected, cumulative asymptomatic and cumulative vaccinated when vaccination rate and inflow level of immigrants are varied.

Parameter | Description | Value | Unity | Reference |
---|---|---|---|---|

$\mathrm{\Pi}$ | Recruitment rate | $\frac{4\times {10}^{8}}{59\times 365}$ | day${}^{-1}$ | Assumed |

$\beta $ | Effective contact rate | $0.09$ | day${}^{-1}$ | Assumed |

v | Vaccination rate | $0.001$ | day${}^{-1}$ | Assumed |

w | Vaccine waning rate | $0.0001$ | day${}^{-1}$ | Assumed |

$\sigma $ | Exit rate from the exposed class | $0.13$ | day${}^{-1}$ | [20] |

$\alpha $ | Prop. of asymptomatic who recover naturally | $0.14$ | day${}^{-1}$ | [20] |

${p}_{s},{p}_{v},{p}_{e},{p}_{i},{p}_{a},{p}_{r}$ | Recruitment prop. into the S, V, E, I, R and A | variable | percentage | |

$\varphi $ | Prop. of exposed who become infected | $0.7$ | day${}^{-1}$ | [21] |

${\tau}_{a}$ | Natural recovery rate of asymptomatic | $0.13978$ | day${}^{-1}$ | [21,22] |

${\tau}_{i}$ | Recovery rate of symptomatic | $0.0833$ | day${}^{-1}$ | [22] |

$\eta $ | Rate at which recovered ind. become suscep. | $0.011$ | day${}^{-1}$ | [23] |

$\xi $ | Reduction in transmission from asymptomatic | $0.3$ | 1 | [21] |

$\mu $ | Natural mortality rate | $\frac{1}{59\times 365}$ | day${}^{-1}$ | [24,25,26] |

$\delta $ | Disease-induced death rate | $0.018/12$ | day${}^{-1}$ | Assumed |

Variables | Description | Initial Value at$\mathit{t}=\mathbf{0}$ | ||

S | Susceptible | 309,974,354 | ||

V | Vaccinated | 0 | ||

E | Exposed | 1,788,800 | ||

A | Asymptomatic | 1,204,000 | ||

I | Infected | 1,204,000 | ||

R | Recovered | 16,462,937 | ||

N | Total population | 330,705,643 |

**Table 2.**Impact of immigration and vaccination on the cumulative infected, cumulative asymptomatic and deaths.

Immigration | Vaccination | Infected | Asymptomatic | Deaths |
---|---|---|---|---|

No | No | 5.372 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ | 1.666 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ | 9.731 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{5}$ |

No | Yes | 3.393 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ | 1.036 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ | 6.392 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{5}$ |

Yes | No | 6.194 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ | 1.949 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ | 1.115 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

Yes | Yes | 3.991 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ | 1.247 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ | 7.440 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{5}$ |

**Table 3.**Impact of immigration and vaccination on the cumulative infected, cumulative asymptomatic and deaths. The SARS-CoV-2 transmission rate considered here is $\beta =0.18$.

Immigration | Vaccination | Infected | Asymptomatic | Deaths |
---|---|---|---|---|

No | No | 4.467 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{8}$ | 1.407 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{8}$ | 8.003 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

No | Yes | 3.669 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{8}$ | 1.154 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{8}$ | 6.621 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

Yes | No | 4.518 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{8}$ | 1.425 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{8}$ | 8.090 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

Yes | Yes | 3.719 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{8}$ | 1.172 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{8}$ | 6.709 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

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**MDPI and ACS Style**

Tchoumi, S.Y.; Rwezaura, H.; Diagne, M.L.; González-Parra, G.; Tchuenche, J.
Impact of Infective Immigrants on COVID-19 Dynamics. *Math. Comput. Appl.* **2022**, *27*, 11.
https://doi.org/10.3390/mca27010011

**AMA Style**

Tchoumi SY, Rwezaura H, Diagne ML, González-Parra G, Tchuenche J.
Impact of Infective Immigrants on COVID-19 Dynamics. *Mathematical and Computational Applications*. 2022; 27(1):11.
https://doi.org/10.3390/mca27010011

**Chicago/Turabian Style**

Tchoumi, Stéphane Yanick, Herieth Rwezaura, Mamadou Lamine Diagne, Gilberto González-Parra, and Jean Tchuenche.
2022. "Impact of Infective Immigrants on COVID-19 Dynamics" *Mathematical and Computational Applications* 27, no. 1: 11.
https://doi.org/10.3390/mca27010011