Analysis of a Vaccination Model for Carrier Dependent Infectious Diseases with Environmental Effects

We have proposed and analyzed a nonlinear mathematical model for the spread of carrier dependent infectious diseases in a population with variable size structure including the role of vaccination. It is assumed that the sus ceptibles become infected by direct contact with infectives and/or by the carrier popula tion present in the environment. The density of carrier population is assumed to be governed by a generalized logistic model and is dependent on environmental and human factors which are conducive to the growth of carrier population. The model is analyzed using stability theory of differential equations and numerical simulation. We have found a threshold condition, in terms of vaccine induced reproduction number R(�) which is, if less than one, the disease dies out in the absence of carriers provided the vaccine efficacy is hi gh enough, and otherwise the infection is maintained in the population. The model also exhibits backward bifurcation at R(�) = 1. It is also shown that the spread of an infectious disease inc reases as the carrier population density increases. In addition, the con stant immigration of susceptibles makes the disease more endemic.