SEASONAL EFFECT ON SIMPLE EPIDEMOIC MODELS
A S Kadi1 and S R Avaradi1
1 Department
of Studies in Statistics, Karnatak University, Dharwad, INDIA 580003.
Email Id: Prof. A.S. Kadi, kadi59as@gmail.com
Abstract
Transmission of infectious diseases often depends on seasonal variability. Seasonal
infections of humans range from childhood diseases, such as measles, chickenpox and
diphtheria, acute diseases caused by the bacteria Caryn bacterium diphtheria, to more faecaloral infections such as cholera and rotaviruses, and vector-borne diseases including malaria.
Some of the causes of seasonality include the ability for the pathogen to survive outside the
host, which depends on the temperature, humidity and exposure to sunlight; host immune
function; the abundance of vectors and non-human hosts.
In this paper we have discussed the seasonal variation for epidemic models like SIR
SEIR for these models we have evaluated seasonal forced function as sinusoidal and term
function. With the help of endemic equilibrium condition for the concept of bifurcation
method, we have calculated the change in state variables and effect in seasonality 𝛽(𝑡)
which provides a powerful and institute visualization of endemic pattern because a key
parameter 𝛽(𝑡) varies with forcing function.
Keywords: Seasonal Effect, Endemic Equilibrium, Bifurcation Method, Epidemic Models.