This presentation discusses viral infections, viral structure and the relationship of viruses to the tree of life. A mathematical model is used to predict when a pandemic may diminish.
Viruses and the Tree of Life. Viruses are infective agents that consist of a nucleic acid molecule covered by a protein coat. Viruses are in a gray area between living and nonliving: they cannot reproduce on their own but they replicate within the living cells of other organisms.
Charles Darwin proposed the theory of evolution in his book The Origin of Species, which was published in 1859. One of his notebooks contained a diagram of a Tree of Life where each branch represented species that diverged from one or more common ancestors. The idea of evolution was controversial in Darwin's time, but it has been firmly established through analysis of DNA molecules that specify the genetic characteristics of all living organisms.
The modern Tree of Life has three domains: Bacteria, Archaea, and Eukarya. Bacteria are microscopic organisms that have shapes ranging from spheres to rods and spirals. Bacteria were the first life forms to appear on Earth, and are present in most of its habitats. Archaea were initially classified as bacteria, but genetic analysis showed that archaea differ significantly from bacteria. Both, bacteria and archaea are called prokaryotes because they have no cell nucleus, mitochondria, or any other structures surrounded by a membrane.
Eukaryotes belong to the domain Eukarya. These organisms have cells walls that contain a nucleus and other genetic material. Eukaryotes may be monocellular like yeasts or multicellular like trees, worms and frogs. The root of the evolutionary tree corresponds to the common ancestor of all life, which gave rise to all organisms now living on Earth.
Viruses are composed of proteins that encapsulate a DNA or RNA genome. These infectious agents replicate only inside the living cells of other organisms and are not included in the Tree of Life. Viruses do not have the ability to reproduce independently. They are thought to be descendants of the diverse chemical entities that developed in the primordial soup that gave rise to life on Earth. The spikes of neuraminidase and hemagglutinin on the surface of a virus enable it to penetrate cell walls to start an infection.
DNA encodes genetic information that corresponds to inheritable traits. DNA forms a double helix in which the nucleotide bases are attached to deoxyribose units linked through phosphate groups. The nucleotide bases in the center of the DNA helix always occur in complementary matched pairs, with cytosine linking to guanine and thymine linking to adenine. James Watson and Francis Crick described the structure of DNA in 1953, and received the Nobel Prize in 1962 for this work.
The mechanism for producing proteins is analogous to offset printing where the image on a printing plate is covered with ink and transferred as a mirror image to a rubber blanket which is then pressed against a sheet of paper to produce the final image. The nucleotide sequence of DNA is not used directly in protein synthesis. Instead, the DNA molecule is transcribed into a complementary sequence of bases, called messenger ribonucleic acid or mRNA, which is then used for protein synthesis. Each set of three nucleic acids in the messenger RNA corresponds to an amino acid in the final protein.
Our bodies fight viral infections by producing antibodies that prevent the replication of the virus. The biological mechanism for producing antibodies is complicated and requires receptors in the cells to produce antibodies for the specific toxins or other foreign substances that induce an immune response.
Viruses are classified based on their nucleic acid constituents and their mode of propagation. A coronavirus, such as COVID-19, consists of a single strand of RNA which acts as messenger RNA to produce proteins for its replication. Viruses are responsible for many diseases, including smallpox, polio, yellow fever, rabies, measles, influenza, and the common cold.
Smallpox had a risk of death of 30 percent, and anyone who survived it was left with a body covered with scars. The first successful vaccine against smallpox was introduced by Edward Jenner in 1796. He observed that milkmaids who had previously caught cowpox did not later catch smallpox. He then showed that inoculation with cowpox protected against smallpox. Smallpox was eradicated in 1980 following a world-wide vaccination campaign. This was possible because humans were the only endemic source of the virus.
Polio or poliomyelitis is an infectious disease caused by the poliovirus. It can cause muscle weakness and paralysis. President Franklin D. Roosevelt was diagnosed with polio in 1921. His memorial in Washington, D.C has a statue of him in a wheel chair. Dr. Jonas Salk developed a vaccine in 1955 that has virtually eliminated the disease from the modern world.
Warts and cold sores are caused by viruses. Once the virus is in your body it is difficult or impossible to eradicate. Measles is a highly contagious viral disease that causes rash all over the body. The virus spreads through the coughs and sneezes of infected people. The measles vaccine is effective in preventing the disease. Children are usually vaccinated against measles at the age of one year with a second dose at age five.
In the past few years, there have been several measles outbreaks in the United States and other countries because some groups of people called anti-vaxxers have opposed vaccination of their children on religious grounds or on the misconception that vaccination causes mental retardation, autism or other maladies. Governments have been trying to enforce vaccination to prevent recurrence of epidemics that put at risk large numbers of people.
Hollywood has dramatized fictional epidemics in films such as Outbreak in 1995. The film describes the outbreak of a virus from a monkey in a military research institute, and speculates how far military and civilian agencies might go to contain the spread of a deadly, contagious disease.
Contagion is a 2011 thriller film that describes the spread of a virus that can be transmitted by touching objects that have been handled by infected individuals. The drama shows medical researchers and public health officials trying to identify and contain the disease, the loss of social order, and the introduction of a vaccine to halt its spread.
Pandemics are characterized by exponential growth. This is a mathematical term. Linear functions are straight lines typically expressed as y = ax + b, where a and b are constants. Exponential functions are graphed as curved lines that constantly increase. An exponential function has an exponent n that determines the rate of growth. Simple interest paid by a bank is an example of a linear function, whereas compound interest is an exponential function.
Mathematical models are used to predict the effects of a pandemic. The rate of transmission and the rate of recovery determine the peak of the infection. For a new virus like COVID-19 all the population is susceptible to the infection. The number of infected people increases as the virus is transmitted to susceptible individuals, but the number of infected people decreases as they recover or die. The peak of the infection indicates the maximum percentage of the population that will be sick at the same time and the burden that will be placed on medical facilities.
The peak of the infection can be flattened by reducing the rate of transmission. This lowers the maximum number of people that will be sick at the same time, and lowers the burden on medical treatment facilities. Notice that as the number of infected people is reduced, some susceptible individuals never get exposed to the virus and never get infected.
The COVID-19 pandemic is the real thing, not a Hollywood fantasy. The number of world-wide infections and deaths are increasing so fast that even a day-old chart is out of date. Pay attention to the exponential curve in the lower right corner that indicates the total number of infections as a function of time.
The COVID-19 infections started in China and the government quickly deployed measures to halt the transmission of the virus. Factories were closed and strict quarantines were imposed. Some videos showed people being forcibly dragged and others were sealed in their apartments by welding shut their apartment doors. Everybody wore face masks. As a result, the number of infections was contained to about 82,000 and about 3000 deaths. That is a death rate of 4 percent. Notice that the curve for the number of infections flattened after an initial exponential growth.
By contrast, Italy has had over 92,000 infections and more than 10,000 deaths. This is a mortality rate of 10.8 percent. Look at the growth curve on the lower right. It seems to be changing from an exponential curve to a linear function, but still there is no sign that the infection rate has been contained and that the curve has started to flatten. South Korea took some early action and is on track to contain the rate of infection. The chart of infections is starting to flatten.
The United States has become the epicenter of the COVID-19 pandemic. Political agendas, medical misinformation and the lack of a nation-wide response have put at risk the whole population. The infection rate is still growing exponentially and medical facilities are already being overwhelmed in large population centers.
The COVID-19 virus has an incubation time of 5.5 days for 97.5% of people infected. People who develop symptoms will do so within 11.5 days of infection. Approximately 80% of the population will recover in 10 days after suffering mild symptoms like fever and cough. Fifteen percent of the population will have more serious symptoms that will require medical care. Five percent of the population will develop life-threatening symptoms that will require hospitalization, the use of oxygen and ventilators. Some of the serious cases will result in death.
Looking at the population of the countries it is easy to see why China took such aggressive measures to contain the virus. Even a mortality rate of one percent would have resulted in 14 million deaths if the whole population had become infected. Now that the United States has become the breeding ground of the COVID-19 pandemic, it will become necessary for China to restrict or quarantine any travelers from the US or other lands where the virus has not been contained to avoid exposing the susceptible population in China. Travel restrictions will have to continue until all countries have reduced the spread of the virus or a vaccine is developed and administered world-wide. This could take several years.
The recommendations to prevent COVID-19 infections are not very different from what they were a century ago for the Spanish influenza. There is no medicine that will prevent infection. People should avoid public meetings. Everyone should keep the mouth and nose covered while coughing or sneezing. Members of the household that become infected should be isolated, and people caring for the sick should wear masks before entering a room with an infected person. This old poster does not mention hand washing, but this is also very important.
The COVID-19 virus spreads by the inhalation of droplets from the coughs and sneezes of infected persons and by touching contaminated surfaces with your hands and then transferring the virus by touching your nose, mouth or eyes. Some medical authorities have been advising that only infected persons should wear face masks, but since the incubation period is at least 5 days, you cannot tell who is infected. During this pandemic we should all wear masks or even cowboy bandanas.