The Critical Proportion of Immune Individuals needed to Control Hepatitis B
Por:
Ospina, J., Hincapié-Palacio, D.
Publicada:
13 may 2016
Resumen:
We estimate the critical proportion of immunity (Pc) to control
hepatitis B in Medellin - Colombia, based on a random population survey
of 2077 individuals of 6-64 years of age. The force of infection (Fi)
was estimated according to empirical data of susceptibility by age S(a),
assuming a quadratic expression. Parameters were estimated by adjusting
data to a nonlinear regression. Fi was defined by -(ds(a)/da)/s(a) and
according to the form of the empirical curve S(a) we assume a quadratic
expression given by S(a)= Ea2+Ba+C. Then we have the explicit expression
for the accumulated Fi by age given by F(a) = -a(Ea+B)/c. The expression
of average infection age A is obtained as A = L + EL3/(3C)+BL2/(2C) and
the basic reproductive number R-0 is obtained as R-0 = 1 +
6C/(6C+2EL2+3BL). From the las result we obtain the Pc given by
Pc=6C/(12C+2EL2+3BL). Numerical simulations were performed with the
age-susceptibility proportion and initial values (a=0.02, b=20, c=100),
obtaining an adjusted coefficient of multiple determination of 64.83%.
According to the best estimate, the algebraic expressions for S(a) and
the Fi were derived. Using the result of Fi, we obtain A = 30, L = 85;
R-0 CI 95%: 1.42 - 1.64 and Pc: 0-0.29. These results indicate that at
the worst case, to maintain control of the disease should be immunes at
least 30% of susceptible individuals. Similar results were obtained by
sex and residential area.
Filiaciones:
Ospina, J.:
Physical Engineering Program, School of Sciences, EAFIT University, Medellín, Colombia
Hincapié-Palacio, D.:
Epidemiology Group, National School of Public Health, University of Antioquia, Medellín, Colombia
|