Modelling the spread of bacterial disease: effect of service providers from an environmentally degraded region

In this paper, an SIS model for bacterial infectious diseases, like tuberculosis, typhoid, etc., caused by direct contact of susceptibles with infectives as well as by bacteria is proposed and analyzed. Here the demography of the human population is constant immigration and the cumulative rate of the environmental discharges is a function of total human population. Further this model is extended to the model for socially structured population (rich and poor) where poor people work as service provider in the houses of rich people but do not settle in the habitat of rich people. It is assumed that bacteria population does not survive in the clean environment of rich people and only affects the population in the degraded environment of the poor class. The stability of the equilibria is studied by using the theory of differential equation and computer simulation. It is concluded that the spread of the infectious disease increases when the growth of bacteria caused by conducive environmental discharge due to human sources increases. Also the spread of the infectious disease in rich class increases due to the interaction with service providers, who are living in relatively poor environmental condition, suggesting the need to keep our environment clean all around. 2003 Elsevier Inc. All rights reserved. * Corresponding author. Present address: Department of Mathematics, University of Trento, Via Sommarive 14, Povo Trento 38050, Italy. E-mail addresses: [email protected] (M. Ghosh), [email protected] (P. Chandra), [email protected] (P. Sinha). 0096-3003/$ see front matter 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2003.11.022 616 M. Ghosh et al. / Appl. Math. Comput. 160 (2005) 615–647