WHY TRY ANALYZING THE NUMBER OF INFECTIONS?

Epidemic modelling is an essential tool for planning future responses to disease outbreaks. By analyzing past and present data, researchers develop mathematical models that predict how many people are likely to become infected. These predictions help governments and health officials decide whether quarantine measures are needed and estimate how quickly action must be taken.

WHAT DATA DO YOU NEED TO CARRY OUT THIS ANALYSIS?

To start with, you need to find out the total number of people who are healthy, but stand at the risk of contracting the disease (say ‘S(t)’). You also need some additional information:-

1. Number of infected people (say ‘I(t)’)
2. Number of immune people (usually the ones who were infected but have now recovered; say ‘R(t)’)

*Note that in the case of some diseases, people who have been infected previously may not stand a better chance of contracting the disease again than a person who has not been infected earlier, but the idea is useful nonetheless.

A RUDIMENTARY MODEL: THE SIR MODEL

Assume that no one is dying due to any cause, i.e., the disease at hand is non-lethal.
Let the total size of the population be N, all of whom are at risk. Then N remains constant by the premise above.

Then, N=S(t)+I(t)+R(t)
Let’s say that 2 people meeting, one infected, the other not, lends a ‘p’ chance of infection to the healthy person, and assume that each person has ‘c’ contacts (contacts include people the infected person meets in 1 day)
Assume that all infected people meet someone according to the rules specified above.
Note that at any time, the fraction of people who are at risk is S(t)/N
Therefore, after 1 day, the number of new infections will be I(t+1)=I(t)[pc][S(t)/N]
Let the mean recovery time be D days (=> there is a 1/D chance of someone recovering each day), then the number of infected people will change per day as

Now modify the timestep to incorporate any change in time, not just one day
So,

Note that transforming this equation into a differential equation then yields (assuming S(t) remains relatively constant, equal to S(0))

Note that if pcDS(0)>N, the number of infected people grows exponentially, and if pcDS(0)<N, the number of infected people decays exponentially, while pcDS(0)=N implies that the number of infected people remains constant.

What does pcDS(0)=N mean, in the context of the disease? It implies a change in the epidemic’s behaviour: a new strain (pattern).

However how would we expect the number of susceptible people to change? It should change as

Why? the term in the brackets represents the proportion of susceptible people which get infected, since this number changes on the basis of the number of infected people at any given time.

Let us examine the above equations in the light of a more general assumption (S(t) changes)

The equations now become

and

This system of coupled differential equations does not have an elementary solution, because dividing both equations cannot recover the time variable in terms of either S(t) or I(t).

However dividing both equations yields the following relationship, (when coupled with the initial conditions I(0)=1, S(0)=N-1)

From here it is easy to see that plugging this relation back into the original equations will not yield an elementary antiderivative to compute I(t) or S(t)

However, we also need to recognize the fact that our disease is non-lethal, and therefore the number of susceptible people also reduces by the amount of recovered people i.e., the factor pc/N changes as pc/(N-R(t))=pc/(I(t)+S(t)) since N-S(t)-I(t)=R(t)

This yields the following implicit solution (obviously no time dependent form because of the complexity)

DISEASE ENDEMICITY AND THE SIS SYSTEM

The SIS system does not impart immunity, and thus non-infected people are simply susceptibles.

The endemic state of a disease is characterized by a steady state solution to the following system of equations

Also, consider the assumption of a vaccine being developed, i.e., introduce a new class V(t), the number of vaccinated individuals.

Let the vaccination rate be ‘$\nu$‘, i.e., people are directly transferred from S(t) to V(t) upon vaccination. Also include fertility as well as mortality at a rate of ‘$\mu$‘

Population conservation:

Final endemic solution:
At equilibrium,

Final recovery solution is the ones where everyone recovers.

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The main reason for aging is a decline in the efficiency of body cells. Over time, due to a host of other factors such as damage due to environment, wrong replication of cells, our cells become much more inefficient. This manifests itself in the form of common signs of aging, which include wrinkles, lethargy and weaker immunity.

A more rigourous treatment of aging yields the following main reasons for such decay:-

1. Damage to our DNA over time
2. The shortening of our telomeres, which serve to protect our DNA. They are small cap like structures on the DNA’s tip, which protect our DNA.
3. Accumulation of old cells that don’t function anymore but don’t die.
4. The decrease in energy output of the mitochondria in our cells.

Can it be prevented?

While it is impossible to prevent such wear and tear of the human body, we can certainly extend it by leading a healthy life. Often age has been linked to genetics- several people may inherit more efficient DNA repair systems, or may even have longer telomere lengths. Apart from these, lack of sleep too can accelerate aging.

The post The science of aging first appeared on Science Wizard.

CAN IT HIT EARTH?

The asteroid was discovered two days after it had already passed its closest point to earth, and it wasn’t detected earlier because it was approaching the earth from the side which isn’t illuminated by the sun.

HOW DO WE CALCULATE ITS TRAJECTORY?

As soon as an asteroid comes into view, we will observe its positions over time. In fact, even if we do not account for the great speeds attained by objects in space, we can still predict the position of any object in the solar system to a good enough degree of accuracy. Consider an object that is 5 million kilometres away from the earth. Such an object is around 10 times further away from the earth than the moon is, and the moon is so far away from Earth that you could fit all the planets of the solar system in the gap between them, and you’d still have ample of space remaining.

WHAT CAN WE DO TO PREVENT AN ASTEROID FROM POTENTIALLY HITTING EARTH?

If such an asteroid was observed, we’d need a timeframe of at least 2 years to do anything. Anything less than that, and we’ll have to roll a dice. After that, we need to deflect its path. For this, even a small projectile can do wonders. We’d have to send a probe in space that would have to collide with the asteroid. Though this will cause quite a small change in its speed, it most probably will be enough, because space itself is quite empty, as illustrated by my earlier argument.

The post 2032: The year of doom for our moon? first appeared on Science Wizard.

HOW DO THEY CAUSE HARM?

Microplastics make their way into our ecosystem through sources ranging from clothing, accessories, food, packaging et cetera. Once we use/consume them, they cause harm because our bodies aren’t well equipped to deal with them, altering our natural processes in the process. Also, they change the functioning of the environment on a large scale, accelerating climate change.

WHAT ARE THEY MADE OF?

Microplastics typically consist of 2 types of chemicals: one are the raw materials, the long branches of complex compounds, along with other additives added to enhance its qualities: resistance to degradation, while the others are the ones which are added to the compound itself with exposure to the environment

WHAT CAN WE DO TO COMBAT THEIR EFFECTS?

Efficient removal of microplastics through waste water treatment plants is necessary to deal with the plastic problem, and we need to find new ways of achieving this. Along with this, all plastic products should be recycled to ensure effective use with minimal environmental risk. lacing an upper cap on plastic production can help immensely as well.

The post The Hidden Plastics first appeared on Science Wizard.

1. Transformer- Converts the electricity it gets (usually 120 volts) to a higher voltage to power the magnetron, which generates microwaves using electricity.
2. This voltage is used to heat up a filament which releases electrons. These high-energy electrons then release microwaves- which are capable of penetrating food, in turn heating it up.
3. The microwave, for visibility, is fitted with a metal mesh which is such that we can see what’s cooking inside the microwave. It is large enough for the microwaves to not escape.
4. Some microwaves have a turntable as well so that all parts of the delicacy can be heated evenly.

EFFECTS OF A MICROWAVE ON FOOD + SAFETY

Although microwaves help heat up food, they also cause the loss of several vital nutrients from food. The insides of food are heated up to abnormally high temperatures which pose the risk of losing almost all nutrients from food.

One must also be quite careful while heating food in microwaves: there is the risk of superheating food, which may have disastrous consequences if human contact takes place. Quite a few liquids may show no signs of boiling while in a microwave, and once disturbed slightly, the boiling might take place suddenly, causing great heat to be released and hence burns.

The post HOW DO MICROWAVES WORK? first appeared on Science Wizard.

RAIN SHADOW

A rain shadow usually is an area behind a mountainous region. While it may be vigorously raining in one area, the side right opposite the mountain may be completely dry. This is also the reason for the Tibetan Plateau being one of the driest places on Earth, since it is right on the other side of the Himalayas.

EXCESS HEAT

As the Earth heats up, air warms up, expands and rises. Due to this, the rising air condenses and pours down as rainfall. This is aggravated by climate change. Also, areas which are warmer than others may end up drawing in convection currents which induce rainfall.

HOWEVER, WHY DOESN’T ALL THE RAIN POUR DOWN ON ONE FLAT AREA?

Let’s say that there are no landscapes to impede rain. Why doesn’t it rain everywhere then? In this case, cloud size becomes a rather dominating factor: it can only rain where a cloud is situated, since clouds store water vapour which eventually pours down. If the cloud isn’t large enough, it may not rain everywhere.

In fact, the rain which falls down onto land is a minute fraction of the rain which starts to come down from the clouds. This is because as the raindrops fall, the air gets hotter and hotter leading to evaporation of the raindrops.

The post RAINING IN ONE PLACE BUT NOT IN THE OTHER first appeared on Science Wizard.

FUN FACTS ABOUT THE GILA MONSTER

1. Their tail acts just like a camel’s hump: it stores fat for later usage.
2. Their venom is used to treat diabetes.
3. They need to hibernate in winters.
4. They don’t need to eat much: they have a meal for a few times in a year
5. They live for around a decade

WHAT’S NEXT IN STORE FOR THEM?

In the hot and humid Mojave desert, Gila monsters are losing their habitats due to climate change (It’s getting too hot for them). It is predicted that a suitable habitat for them will change over time, and their winter hibernation period is set to extend.

The post GILA MONSTERS first appeared on Science Wizard.

Potash includes various salts that contain potassium, the element, in its water-soluble form. It’s named after “pot ash”, a nod to an old way of making it, which involved burning wood ashes in pots before adding water to form lye. Lye, when evaporated, gave potash.

HOW IS IT EXTRACTED NOWADAYS?

Nowadays we get potash from underground shaft mining, which involve underground tunnels, or from salt lakes (which were part of very old dried up oceans)

WHAT IS IT USED FOR?

While making glass, you require lots of silica dioxide (SiO₂), which has a very high melting point. Adding potash reduces its melting point, which strengthens the glass.
Adding manure to a potash solution gives potassium nitrate, an integral component of fireworks. Potash can also be obtained from rocks, and is used in fertilizers as well.

The post POTASSIUM first appeared on Science Wizard.

You must have been taught this “tongue map” some time in school.

This tongue map labels certain parts of the tongue, and states them to be responsible for different taste sensations (1-> bitter, 2-> sour, 3-> salty and 4-> sweet)

Actually, this is false.

This theory originated from a book written by Edwin Boring in 1942, where he plotted the taste thresholds for different parts of the tongue. This graph was misinterpreted by other authors, who started to believe that the tongue did not sense anything for a particular taste in a particular region, when the region represented merely a minima in the graph.

This theory was then so widely circulated that tongue map experiments (wherein participants had to record intensities of different tastes by placing food on different regions of the tongue) were used to grade high school students.

It was debunked in 1974 by Virginia Collings, who confirmed that taste exists on all parts of the tongue.

The post HOW DO WE TASTE? ADDRESSING COMMON MISCONCEPTIONS ABOUT THE TONGUE first appeared on Science Wizard.

Drooling is when saliva flows out of the mouth involuntarily. This is natural, and mostly occurs when you don’t have much control, i.e., when you sleep. This occurs when you swallow less, which leads to more saliva in your mouth.

Is it an issue? If yes, how can it be treated?

Excessive drooling may be caused due to allergies. To flush the excess toxins out, excess saliva is produced, causing you to drool. If accompanied by itchy eyes and a runny nose, seasonal allergies are the culprit. Infected sinuses may cause problems as well, which cause a blockage and lead to drooling.

For treating excessive drooling, visit your nearest ENT specialist. Medication is required. Maintain a constant intake of fluids. In severe cases, treatment of salivary glands may be required.

Excessive drooling may also be caused by a disorder known as sleep apnea, which can be of two forms: Obstructive (airway blockage) and Central (when the brain isn’t sending the signals needed to breathe)

The post DROOLING WHILE WAKING UP? first appeared on Science Wizard.