See in Disease transmission especially communicable diseases like HIV-AIDS, Polio etc. are segmented in various segment.
One is through
Person to Person Contact - Like HIV AIDS, the disease transmits if infected blood is transfused unknowingly, sexual transmission or from mother to child. Similarly Swine Flue and many Viral diseases. Polio is a Viral disease
Vector borne diseases - Cholera, Dengue which spreads due to Flies, Mosquitoes where these are modes of transmission that infect people.
Environmental factors affect a lot in transmission of disease. You would be pleased to know that India has done extensive research in this field and India is credited for highlighting it as major factor in study of Epidemics.
Now lets come to Polio. Its a SIS disease with a class of Vaccinated people. This means there are susceptible (S), infected (I) and Vaccinated (Polio Dose administered). If vaccinated children are not properly vaccinated again they may become susceptible to Polio.
Let
total Population be N. It includes entire children population of a region.
N = S + I + V . Lets say in a region there is 0 infected person and no children is vaccinated. So
S=N, I= 0 , V = 0. (N,0,0).
In case of
No vaccination.
Now if even one child has polio,
I=1, S =N-1, V=0. So the disease will spread to total children population if there is no segregation of infected children and the disease will reach the state of
S=0,I=N,V=0. (0,N,0). This is the stability state of Disease transmission in a population system.
Now if we start Vaccination program,
S ----> V class and won't go to I class. So if we have effective vaccination program and control, the system will reach
S=S*,I=I*,V=V*. This is a stable equilibrium.
Our aim is bring I*=0. So we need complete vaccination of
Susceptible (S)-------> Vaccinated (V) so that S=0, V=0
Since N=S+I+V, and we wanted to achieve I=0. S=0, V= N.
Now to drive people to take their children for administration of Polio drops, we run awareness campaign, we used Amitabh Bacchan for Media and our TV Channels, Radio and Newspaper. We organized Polio Drops Drive and went to door to door in major affected region.
So for making S=0, I=0, we need effective Awareness program to take S ----- > V Class.
Now in case of Pakistan, the terrorist threats and killing of Polio worker, lack of resources and lack of awareness and doubts among people, its hard to Transition from S to V so that S=0,I=0, V=N become reality
There are many Mathematical equations but it will bore you all.
P.S. - Professionals and Doctors may not agree with the terminology used, but I simplified it for better understanding.