Analysis of a model for carrier dependent infectious diseases with sanitation as a control strategy

Abstract

The sanitation plays a very important role to control the spread of infectious diseases and is much effective public health intervention. Inadequate sanitation is a major cause of spread of carrier dependent infectious diseases such as typhoid, dysentery and cholera. In this paper, a nonlinear mathematical model is proposed to study the effect of sanitation on the spread of such diseases in a homogeneously mixed human population. In modeling the process, it is assumed that the disease spreads directly from the infectives to susceptibles as well as indirectly by the carriers present in the environment. The density of carrier population is assumed to grow logistically but it declines due to sanitation effort applied whereas the sanitation effort also follows a logistic model with its desired increase taken directly proportional to the density of carrier population. The proposed model is also extended to an optimal control problem and is analyzed using Pontryagin Maximum Principle. The model analysis reveals that the carrier population density decreases with increase in the sanitation effort applied resulting to decrease the infective population and hence decline in the disease prevalence. Thus, the spread of carrier dependent infectious diseases can be controlled significantly if suitable sanitation effort is applied to curb the carrier population in the environment. Numerical simulations performed also support the analytical findings.

Keywords

• mathematical model
• infectious diseases
• carrier population
• sanitation effort
• stability
• numerical simulation