Question

PROJECT Modeling the Dynamics of Viral Infections Chris Bjarnberg/Science Source A patient is infected with a virus that triples its numbers every hour. The immune system eventually kicks in and reduces the replication rate by a factor of in addition to kill- ing 500,000 virus particles per hour, but this doesn't happen until the viral load reaches two million copies. To combat the infection, the infected person receives hourly doses of an antiviral drug. This drug further reduces the replication rate, to a value of 1.25, and the immune system and the drug together can kill 25,000,000 copies of the virus per hour. Let's model the phases of the infection using a discrete-time difference equation. 1. What is the recursion for the number of viral particles in the absence of treatment and before the immune response starts? What is the equation for the number of viral particles as a function of time? 2. How long does it take for the immune system to be activated after the infection starts? Derive an equation for this length of time for an arbitrary initial number of viral particles. 3. What is the recursion for the number of viral particles after the immune response has begun, but before the drug is used? 4. What is the condition for the viral population size to decrease over time solely because of the immune system? Is this possible? 5. What is the recursion for the number of viral particles in the presence of both the immune response and the drug? 6. What is the condition for the viral population size to decrease over time when the drug and immune system are both acting? Is this possible? 7. If an individual is infected by one virus, how much time do you have to start drug treatment in order to control the infection? 8. Often the outcome of an infection depends on the number of viral particles causing the infection. Derive an expression for the amount of time it takes from the initial infection for an individual to reach the critical viral load-beyond which control of the infection is impossible—as a function of the initial number of particles no and an arbitrary initial replication rate R.

Answer 1

0. Wenen a virus infects a person (hoos) It invades the wes of is host in order to survive and replicate. once, inside, the wes of the Germune system cannot see the virus and therefore do not know that the chost all is infected. → yo overcome anis, aus empray a system that allows them to share other aus what is inside them - they use moucules called class I major histocompatiility complen proteins cor Mhe class i, for short) to display pieces of protein from inside the can Spon the cell surface. → For a certain rus, the equation 9 Lt) = soe.35t, where it is the time an hour and oo is the onereal number of verus particles, y peeds the number of verus particles as a function of time.

2. The emmune system rests on two major mars: the innate general immune system and the adaptive, specialexed emmune system. Both systems work closely together and take on different tasks La bacteria orveruses manage to enten the body they can be cuminated directly on the spot by scanengerceus or phagocytes two types of defense aus are the most effective ones: ones. macrophages, nenech are found in the tissues and neutrophie granulocyles, which are in the blood and . فلیممشد " of the body's first line of defense- the innate immune system - is unsucceful in destroying the pathogens, after about your to senen days the specific adapun ermune response sets in this means that the adaptue defense takes longer, sout it targets the pathogen more