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In spite of local and international efforts to end the scourge of poliomyelitis in the world, the disease still exists around the world with new cases being detected in otherwise polio-free areas while the known endemic places of Asia and Sub-Saharan Africa are yet to be ridden of the epidemic. Knowing with accuracy whether the disease has finally ended in a population has always being a subject of interest to mathematicians, statisticians and epidemiologists. In this study, we have defined a conditional probability function xic(t) as the probability of zero transmission agents given that there are initially (i) symptomatic (ii) infectives and (iii) asymptomatic carriers. Using the properties of Poisson process, two backward equations were derived which were jointly solved numerically. With these numerical solutions, we were able to formulate a model for the two identified transmission agents of poliomyelitis. [ABSTRACT FROM AUTHOR]

Eradicating poliomyelitis has been a major health concern to stakeholders the world over. In this study, we have developed a pair of stochastic equations for the extinction probability functions in two types of human transmission agents namely: infectives (types 1) and carriers (type 2). By solving the equations, the result shows that with only one asymptomatic carrier in a population, eradication is possible when (β22 + β21_µ)2 > 4β22µ where βij is the Poisson rate at which type i transmission agent produces type j transmission agent and β is the mean infectious period of the asymptomatic carriers. [ABSTRACT FROM AUTHOR]