Modeling the effect of sanitation in a human habitat to control the spread of bacterial diseases

Abstract

The improper and poor sanitation, unclean drinking water and lack of hygiene are the key factors that affect the spread of various infectious diseases such as tuberculosis, typhoid fever,and cholera. In this paper, the effect of sanitation effort to control the spread of bacterial diseases is modeled and analyzed. In the modeling process, the total human population in the habitat is divided into two classes of susceptibles and infectives. The disease is assumed to spread directly by contact of susceptibles with infectives and indirectly by bacteria released by infectives in the environment affecting the susceptibles. It is assumed that the bacterial population density is directly proportional to the infective population. To mitigate the bacteria population present in the environment, suitable sanitation effort is applied to keep the environment clean so that the spread of disease could be controlled. The sanitation effort applied is modeled logistically, the intrinsic growth of which is assumed to be directly proportional to the density of bacteria present in the environment. The proposed model is analyzed using the stability theory of differential equations and numerical simulation. The analysis of the model reveals that by increasing the rate of sanitation effort, the bacteria population in the environment declines. This decrease in bacteria population in the environment ultimately decreases the infective population. Thus, the spread of bacterial diseases can be controlled if suitable sanitation effort is applied to curtail the bacterial population in the environment.