Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation
| Autor: | Edwin Mauricio Carranza-Mayorga, Hernán Darío Toro-Zapata, Carlos Andrés Trujillo-Salazar |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
delay differential equations
Differential equation Population Bioengineering lcsh:Chemical technology 01 natural sciences Stability (probability) 010305 fluids & plasmas Quantitative Biology::Cell Behavior lcsh:Chemistry materials_science_other 0103 physical sciences Chemical Engineering (miscellaneous) Applied mathematics lcsh:TP1-1185 0101 mathematics education Mathematics education.field_of_study Computer simulation Process Chemistry and Technology 010102 general mathematics HIV Delay differential equation immune system lcsh:QD1-999 Ordinary differential equation Basic reproduction number Viral load mathematical model |
| Zdroj: | Processes Volume 8 Issue 7 Processes, Vol 8, Iss 782, p 782 (2020) |
| ISSN: | 2227-9717 |
| DOI: | 10.3390/pr8070782 |
| Popis: | A mathematical model, composed of two non-linear differential equations that describe the population dynamics of CD4 T cells in the human immune system, as well as viral HIV particles, is proposed. The invariance region is determined, classical equilibria stability analysis is performed using the basic reproduction number, and numerical simulations are carried out, in order to illustrate stability results. Later, the model is modified with a delay term, which describes the time that cells require for immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations, via auxiliary variable use. For the new model, equilibrium points are determined, their local stability is examined, and results are studied by way of numerical simulation. |
| Databáze: | OpenAIRE |
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