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Abstract

We have proposed and analyzed a nonlinear mathematical model for the spread of bacterial disease in an economically structured population (rich and poor) including the role of vaccination. It is assumed that rich susceptible get infected through direct contact with infectives in the same class and with infectives from the poor class who work as service providers in the houses of rich people, living in much cleaner environment. The susceptible in the poor class are assumed to become infected through direct contact with infectives in the same class as well as by bacteria present in their own environment, degraded due to unhygienic environmental conditions. It is further assumed that the bacteria population affects only the population in the degraded environment of the poor class but does not survive in the clean environment of rich people. The density of bacteria population is assumed to be governed by a logistic model and is dependent on environmental discharges conducive to the growth of bacteria population. The cumulative density of environmental discharges depends upon the human population related factors of the poor class. The model analysis shows that the increased growth rate of environmental discharges increases the bacteria population density in the poor class due to unhygienic environmental conditions leading to increase the infectives in the poor class i.e., service providers. As a consequence, due to interaction with these service providers the spread of disease increases in the rich class. The improved environmental conditions of the region inhabited by service providers along with suitable vaccination strategy can be helpful in reducing the spread of the disease.

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