Modeling cancer in hiv-1 infected individuals: equilibria, cycles and chaotic behavior

Jie Lou1, Tommaso Ruggeri, Claudio Tebaldi

  • 1Department of Mathematics, Shanghai University, 99 Shangda Road Shanghai 200444, P. R. China. jie.lou@126.com.

Related Concept Videos

Retrovirus Life Cycles01:10

Retrovirus Life Cycles

Retroviruses have a single-stranded RNA genome that undergoes a special form of replication. Once the retrovirus has entered the host cell, an enzyme called reverse transcriptase synthesizes double-stranded DNA from the retroviral RNA genome. This DNA copy of the genome is then integrated into the host’s genome inside the nucleus via an enzyme called integrase. Consequently, the retroviral genome is transcribed into RNA whenever the host’s genome is transcribed, allowing the retrovirus to...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Mechanisms of Retrovirus-induced Cancers01:51

Mechanisms of Retrovirus-induced Cancers

Retroviruses are RNA viruses that have been shown to cause cancers in diverse species, including chickens, mice, cats, and monkeys. The RNA genomes of these viruses are first reverse-transcribed into single and then double-stranded DNA (dsDNA) copies. This dsDNA called proviral DNA then integrates into the host genome. Subsequently, the host cell transcribes the proviral DNA in concert with the chromosomal DNA. This leads to the production of viral RNA and proteins that assemble at the host...
Mechanisms of Retrovirus-induced Cancers01:51

Mechanisms of Retrovirus-induced Cancers

Retroviruses are RNA viruses that have been shown to cause cancers in diverse species, including chickens, mice, cats, and monkeys. The RNA genomes of these viruses are first reverse-transcribed into single and then double-stranded DNA (dsDNA) copies. This dsDNA called proviral DNA then integrates into the host genome. Subsequently, the host cell transcribes the proviral DNA in concert with the chromosomal DNA. This leads to the production of viral RNA and proteins that assemble at the host...
Tumor Progression02:07

Tumor Progression

Tumor progression is a phenomenon where the pre-formed tumor acquires successive mutations to become clinically more aggressive and malignant. In the 1950s, Foulds first described the stepwise progression of cancer cells through successive stages.
Colon cancer is one of the best-documented examples of tumor progression. Early mutation in the APC gene in colon cells causes a small growth on the colon wall called a polyp. With time, this polyp grows into a benign, pre-cancerous tumor. Further...
What is Cancer?02:12

What is Cancer?

Cells and tissues must meticulously coordinate their activities for the normal functioning of the human body. Therefore, they exhibit socially responsible behavior - resting, growing, dividing, differentiating, or dying - for the organism’s benefit. Cancer arises when cells divide uncontrollably and invade other tissues or organs.
Although people have known about cancer for centuries, it was only in 1761 that Giovanni Morgagni of Padua performed a detailed autopsy of patients who died from...