Modeling the dynamics of viral infections in presence of latently infected cells

doi:10.1016/j.chaos.2020.109916

. 2020 Jul:136:109916.

doi: 10.1016/j.chaos.2020.109916. Epub 2020 Jun 4.

Modeling the dynamics of viral infections in presence of latently infected cells

Khalid Hattaf^{1

2}, Hemen Dutta³

Affiliations

¹ Centre Régional des Métiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco.
² Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik, Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco.
³ Department of Mathematics, Gauhati University, Guwahati 781014, India.

PMID: 32518473
PMCID: PMC7271877
DOI: 10.1016/j.chaos.2020.109916

Modeling the dynamics of viral infections in presence of latently infected cells

Khalid Hattaf et al. Chaos Solitons Fractals. 2020 Jul.

. 2020 Jul:136:109916.

doi: 10.1016/j.chaos.2020.109916. Epub 2020 Jun 4.

Authors

Khalid Hattaf^{1

2}, Hemen Dutta³

Affiliations

¹ Centre Régional des Métiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco.
² Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik, Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco.
³ Department of Mathematics, Gauhati University, Guwahati 781014, India.

PMID: 32518473
PMCID: PMC7271877
DOI: 10.1016/j.chaos.2020.109916

Abstract

The study aims to develop a new mathematical model in order to explain the dynamics of viral infections in vivo such as HIV infection. The model includes three classes of cells, takes into account the cure of infected cells in latent period and also incorporates three modes of transmission. The mention modes are modeled by three general incidence functions covering several special cases available in the literature. The basic properties of the model as well as its stability analysis have been carried out rigorously. Further, an application is given and also numerical simulation results have been incorporated supporting the analytical results.

Keywords: Asymptotic stability; Latently infected cells; Mathematical modeling; Viral infection.

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Conflict of interest statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figures

**Fig. 1**
Schematic diagram of model (1).

**Fig. 2**
Dynamics of the model (10) when $R_{0} = 0.9733 < 1$ .

**Fig. 3**
Dynamics of the model (10) when $R_{0} = 6.7313 > 1$ .

**Fig. 4**
Dynamics of the model (10) when $R_{0} = 7.6442 > 1$ .

See this image and copyright information in PMC

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References

1. Agosto L.M., Herring M.B., Mothes W., Henderson A.J. HIV-1-infected CD4 $^{+}$ T cells facilitate latent infection of resting CD4 $^{+}$ T cells through cell-cell contact. Cell Rep. 2018;24(8):2088–2100. - PubMed
1. Carr J.M., Hocking H., Li P., Burrell C.J. Rapid and efficient cell-to-cell transmission of human immunodeficiency virus infection from monocyte-derived macrophages to peripheral blood lymphocytes. Virology. 1999;265:319–329. - PubMed
1. Callaway D.S., Perelson A.S. HIV-1 infection and low steady state viral loads. Bull Math Biol. 2002;64:29–64. - PubMed
1. Chen P., Hubner W., Spinelli M.A., Chen B.K. Predominant mode of human immunodeficiency virus transfer between T cells is mediated by sustained Env-dependent neutralization-resistant virological synapses. J Virol. 2007;81:12582–12595. - PMC - PubMed
1. Dimitrov D.S., Willey R.L., Sato H., Chang L.J., Blumenthal R., Martin M.A. Quantitation of human immunodeficiency virus type 1 infection kinetics. J Virol. 1993;67(4):2182–2190. - PMC - PubMed

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[1] Agosto L.M., Herring M.B., Mothes W., Henderson A.J. HIV-1-infected CD4 $^{+}$ T cells facilitate latent infection of resting CD4 $^{+}$ T cells through cell-cell contact. Cell Rep. 2018;24(8):2088–2100. - PubMed

[2] Agosto L.M., Herring M.B., Mothes W., Henderson A.J. HIV-1-infected CD4 $^{+}$ T cells facilitate latent infection of resting CD4 $^{+}$ T cells through cell-cell contact. Cell Rep. 2018;24(8):2088–2100. - PubMed

[3] Carr J.M., Hocking H., Li P., Burrell C.J. Rapid and efficient cell-to-cell transmission of human immunodeficiency virus infection from monocyte-derived macrophages to peripheral blood lymphocytes. Virology. 1999;265:319–329. - PubMed

[4] Carr J.M., Hocking H., Li P., Burrell C.J. Rapid and efficient cell-to-cell transmission of human immunodeficiency virus infection from monocyte-derived macrophages to peripheral blood lymphocytes. Virology. 1999;265:319–329. - PubMed

[5] Callaway D.S., Perelson A.S. HIV-1 infection and low steady state viral loads. Bull Math Biol. 2002;64:29–64. - PubMed

[6] Callaway D.S., Perelson A.S. HIV-1 infection and low steady state viral loads. Bull Math Biol. 2002;64:29–64. - PubMed

[7] Chen P., Hubner W., Spinelli M.A., Chen B.K. Predominant mode of human immunodeficiency virus transfer between T cells is mediated by sustained Env-dependent neutralization-resistant virological synapses. J Virol. 2007;81:12582–12595. - PMC - PubMed

[8] Chen P., Hubner W., Spinelli M.A., Chen B.K. Predominant mode of human immunodeficiency virus transfer between T cells is mediated by sustained Env-dependent neutralization-resistant virological synapses. J Virol. 2007;81:12582–12595. - PMC - PubMed

[9] Dimitrov D.S., Willey R.L., Sato H., Chang L.J., Blumenthal R., Martin M.A. Quantitation of human immunodeficiency virus type 1 infection kinetics. J Virol. 1993;67(4):2182–2190. - PMC - PubMed

[10] Dimitrov D.S., Willey R.L., Sato H., Chang L.J., Blumenthal R., Martin M.A. Quantitation of human immunodeficiency virus type 1 infection kinetics. J Virol. 1993;67(4):2182–2190. - PMC - PubMed

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Modeling the dynamics of viral infections in presence of latently infected cells

Affiliations

Modeling the dynamics of viral infections in presence of latently infected cells

Authors

Affiliations

Abstract

Conflict of interest statement

Figures

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References

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