**Basic Reproductive Ratio**The basic reproductive ratio, pronounced as R-nought is defined.

await a number of second germs arising from a single.

the single during his or her entire virus period.

number of days an infected person remains infective and the number

of susceptible persons available to infect This concept is fundamental to the study of epidemiology.

**In biology what is
the basic is the reproductive ratio?**

It is like a fundamental
concepts of mathematical ratio biology
defined the number of seconds infections caused by a signal individual R0

.

**Rate of reproductive
ratio? **

** **

The number is R0ALSO called the ratio the incidence metric describes the infectious agents.

reproductive of infection is
bodily fluids 1.5 – 2.5 in epidemiology called basic reproductive ratio or
incorrectly basic reproductive rate and denoted R0, r naught cases generates on average over the course of
its epidamic period in an otherhand fresh crowd.

History of Ro

Originally developed for demographics in 1886

And 1911 and 1927 is
independently studied malaria and in
1975+ now widely used for injections disease.

** Heesterbeek & dietz 1996 says that one of
the most valuable ideas that mathematical thinking has brought to the epidemic
theory.**

** **

·
**In it is individual lifetime they produced expected numbers of secondary individuals.**

·
**Secondary means lifetime demographics and ecology and
number of individuals infected within a single infected individual entire
infections lifetime epidemiology.**

· ** viruses cells produced by a single
infected cell in host dynamics.**

·
**If there R0<1 then each individual produces on
average less than one new and hence the disease
dies out**

·
**And if there is R>1 then each individual produces
more than one new infected individuals on that time the disease is able to invade
the susceptible population in our country.**

·
**Determines the effectiveness of control of measures.**

·
**R0 is a threshold we predict whether a disease will
came endemic or die out**

·
**If R0 is R0>1 then each individual is causing more than one
infection, so the disease will take hold of that **

·
**If R0 is the threshold and R<1 then the disease will die out and most important in a threshold is where R0
is most useful**

·
**Ro is rarely measured in the field and Ro is an individual
parameter, eg ODEs deal with populations matching the two and lots of thresholds
, not necessarily the true Ro.**

·
**These surrogate, R0 like thresholds will also tell
us whether a disease will become endemic or die out and they may be easier to
calculate than the true R0 but it is different diseases.**

·
**Suppose HIV has an R0 of 2 and covid -19 has a Ro
of 2.5, unless they were calculated using the same method, we do not know if
covid 19 is worse than HIV and we know
that both will persist because Ro is a distance
measure and thus dependent on the metric used **

·
**Concepts of Anderson and May,**

·
**R0= b c d where
B= transmission probability **

·
**C= number of contacts per unit time**

·
**D= average time spent infectious is the method by biologists not always correctly **

·
** THE JACOBIAN**

·
** A matrix of partial
derivatives, created by different every equation with respect to every
variable and 6 equations and 6 variables and you will have 6 into 6 matrix**

·
** Calculate the disease of free equilibrium and the jacobian matrix after that evaluate the
jacobian at the equilibrium and after that find the eigenvalues if all eigenvalues
< 0 = stable even one eigenvalue >0 = unstable and largest eigenvalue = r0 like threshold
and use the real part.**

·
**R0 sis <1 we have the stability of the DFE and hence
the disease dies out.**

** **

**
If R 0 sis >1 we have instability of the DFE and hence the disease
persists but R 0 is still can not define.**

** Mathematic way answer is **

**{ Ro SIS }squre < 1 = dies out
with diseases**

**[ Ro SIS ] square > 1 disease
persists.**

**SIS model is threshold sleight of hand Ro **

** There is no reason the largest eigenvalue
would inexorably lead to the average number of infections**

** **

** **

**Ro is not defined for ODEs, but we want to threshold then it
will acceptable, there are so many methods of calculating that ratio.**

**
SIS endemic equilibrium**

** **

** The endemic equilibarium for the SIS model is
b/a , n-b/a >0 **

** **

** N >b/a**

** Define R0 end = a N/b**

** As before
[ since if Ro end >1 , the disease
persists**

** N = Total app **

**A= infection rate of sis**

**B=recovery rate**

** **

** **

**The gold standard of Ro
* complete cycle of account of dengue**

**Not restricted to ODEs but can get cucumber some for multiple states just of
particle use we know scrapie in Cyprus (
Gravenor at 2004, dengue in brazil in 2003**

** **

** **

** The next generation of method**

** A general type of deriving Ro when the population
is divided Into discrete, disjoint cases
will be used as a model with
underlying age people.**

** **

** **

**What is the mean of “generation” **

**The number of infected humans produced
by a single infected human of all time
and next generation of infected mosquitos produced by a single human **

** **

** In partical : west nile virus { wonham 2004 } mad cow {
2003} **

** **

** More updates will come in this article.**

__Recent world days__

Thanks for reading and watching this and do share more reach and give your valuable feedback 👉🏻👉🏻👉🏻👉🏻👉🏻 below

## 0 Comments:

thanks for your feedback