#
Singly Diagonally Implicit Block Backward Differentiation Formulas for HIV Infection of CD4^{+}T Cells

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## Abstract

**:**

## 1. Introduction

## 2. Singly Diagonally Implicit Block Backward Differentiation Formulas

## 3. Results of Numerical Simulation

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The two-point Singly Diagonally Implicit Block Backward Differentiation Formulas (SDIBBDF) method of constant step size.

Dependent variables | ||
---|---|---|

T | Uninfected CD${4}^{+}$T cells population size | |

I | Infected CD${4}^{+}$T cells density | |

V | Initial density of HIV RNA | |

Parameters & constants | ||

$\lambda $ | Source term for uninfected CD${4}^{+}$T cells | $1.0\times {10}^{-1}$ day${}^{-1}$ mm${}^{-3}$ |

$\mu $ | Natural death rate of CD${4}^{+}$T cells | $2.0\times {10}^{-2}$ day${}^{-1}$ |

r | Growth rate of CD${4}^{+}$T cells population | 3 day${}^{-1}$ |

${\mathit{T}}_{\mathit{max}}$ | Maximal population level of CD${4}^{+}$T cells | $1.5\times {10}^{3}$ mm${}^{-3}$ day${}^{-1}$ |

k | Rate of CD${4}^{+}$T cells become infected with virus | $2.7\times {10}^{-3}$ mm${}^{-3}$ |

$\rho $ | Blanket death rate of infected CD${4}^{+}$T cells | $3.0\times {10}^{-1}$ day${}^{-1}$ |

N | Number of virions produced by infected CD${4}^{+}$T cells | 10 mm${}^{-3}$ |

$\tau $ | Death rate of free virus | $2.4$ day${}^{-1}$ |

t | SDIBBDF | BBDF | RK4 | EULER |
---|---|---|---|---|

0.0 | 0.1000000000000000 | 0.1000000000000000 | 0.1000000000000000 | 0.1000000000000000 |

0.2 | 0.2090205532222125 | 0.2162665954333766 | 0.2087297222454430 | 0.2066396850000000 |

0.4 | 0.4065545236060797 | 0.4050981887697551 | 0.4059409955447710 | 0.3455020000000000 |

0.6 | 0.7648420298033937 | 0.7365813304773389 | 0.7635801781341750 | 0.6050020000000000 |

0.8 | 1.4145067965307667 | 1.3965775540613832 | 1.4119574363577000 | 1.0420600000000000 |

1.0 | 2.5840259154129843 | 2.3865826219889092 | 2.5867778755778800 | 1.7779900000000000 |

t | SDIBBDF | BBDF | RK4 | EULER |
---|---|---|---|---|

0.0 | 0.1000000000000000 | 0.1000000000000000 | 0.1000000000000000 | 0.1000000000000000 |

0.2 | 0.0619225726474935 | 0.0638429946616157 | 0.0618798121706440 | 0.0577610000000000 |

0.4 | 0.0383177394040220 | 0.0385396728096125 | 0.0382948730759080 | 0.0333660000000000 |

0.6 | 0.0237164781782014 | 0.0244736504530348 | 0.0237045402752520 | 0.0192790000000000 |

0.8 | 0.0146863853079351 | 0.0147827377616151 | 0.0146803506585660 | 0.0111450000000000 |

1.0 | 0.0091490338084673 | 0.0094989136071827 | 0.0091008270878710 | 0.0064500000000000 |

t | SDIBBDF | BBDF | RK4 | EULER |
---|---|---|---|---|

0.0 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000 |

0.2 | 0.0000060459344453 | 0.0000058406917327 | 0.0000060315204770 | 0.0000059531387000 |

0.4 | 0.0000131823896412 | 0.0000130303451230 | 0.0000131530315000 | 0.0000128846300000 |

0.6 | 0.0000212573455944 | 0.0000214442550764 | 0.0000212106240460 | 0.0000206134400000 |

0.8 | 0.0000302184570008 | 0.0000302550927739 | 0.0000301518386990 | 0.0000290605600000 |

1.0 | 0.0000399547343565 | 0.0000382633892925 | 0.0000399942614780 | 0.0000382160400000 |

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**MDPI and ACS Style**

Jana Aksah, S.; Ibrahim, Z.B.
Singly Diagonally Implicit Block Backward Differentiation Formulas for HIV Infection of CD4^{+}T Cells. *Symmetry* **2019**, *11*, 625.
https://doi.org/10.3390/sym11050625

**AMA Style**

Jana Aksah S, Ibrahim ZB.
Singly Diagonally Implicit Block Backward Differentiation Formulas for HIV Infection of CD4^{+}T Cells. *Symmetry*. 2019; 11(5):625.
https://doi.org/10.3390/sym11050625

**Chicago/Turabian Style**

Jana Aksah, Saufianim, and Zarina Bibi Ibrahim.
2019. "Singly Diagonally Implicit Block Backward Differentiation Formulas for HIV Infection of CD4^{+}T Cells" *Symmetry* 11, no. 5: 625.
https://doi.org/10.3390/sym11050625