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The AIDS is a chronic disease and the researchers still exert their high efforts to reach the cure of HIV infection. The most common treatment is the antiretroviral therapy (cART) and the virus can be more effected if the patients stop using cART. The other problem is that the CD8+ T cells might be exhausted by persistent immune activation by cART. This paper introduces fractional-order into a mathematical model of HIV infection combining with stem cell therapy and control the infection by the immune system cells (CD8+ T cells). The paper introduced the numerical solutions for the mathematical model. The results show that the stem cell therapy with the activation of immune system cells might causes the cure for a HIV patient. This results are consistent with medical studies. Also, we proposed the effect of the fractional order (α) on the figures of the components. [ABSTRACT FROM AUTHOR]

Ebola virus (EBOV) targets immune cells and tries to inactivate dendritic cells and interferon molecules to continue its replication process. Since EBOV detailed mechanism has not been identified so far, it would be useful to understand the growth and spread of EBOV dynamics based on mathematical methods and simulation approaches. Computational approaches such as Cellular Automata (CA) have the advantage of simplicity over solving complicated differential equations. The spread of Ebola virus in lymph nodes is studied using a simplified Cellular Automata model with only four parameters. In addition to considering healthy and infected cells, this paper also considers T lymphocytes as well as cell movement ability during the simulation in order to investigate different scenarios in the dynamics of an EBOV system. It is shown that the value of the probability of death of T cells affects the number of infected cells significantly in the steady-state. For a special case of parameters set, the system shows oscillating dynamics. The results were in good agreement with an ordinary differential equation-based model which indicated CA method in combination with experimental discoveries could help biologists find out more about the EBOV mechanism and hopefully to control the disease. [ABSTRACT FROM AUTHOR]