Congenital Transmission of Chagas with Control Dropouts and Spraying

Vector-borne diseases are the leading causes of death amongst all disease. They remain as highest risk for lives of millions of people in many countries of the world. Scientific and economic impacts of vector-borne disease are significant. Chagas is one of the vector-borne diseases found in Latin American countries with its large impact. Studies indicate that vector control is the most convergent way to control vector-borne diseases. To control vectors, spraying insecticide is the easiest and safest way, but sometimes it is cost worthy for long period of spraying. Also, for most of the Vector-borne diseases treatments are available, but because of unawareness they spread at high frequency. People may start to opt the treatment but the side effects or cost of treatment, force them to left treatment in between and that create larger dropouts. Vertical transmission of disease also plays vital role in spreading disease as it increases infected population. As costs are incorporated with spraying and dropout both and our aim is to minimise the total cost associated by controlling both spraying and drop-out in a way spraying should be maximum and dropout should be minimum for disease control. With this purpose for chagas disease a mathematical model is suggested with disease dynamics in ten compartments namely Susceptible treated human child, Susceptible untreated human child, Susceptible treated human adult, Susceptible untreated human adult, Infected treated human child, Infected untreated human child, Infected treated human adult, Infected untreated human adult, Susceptible vector and infected vector including vertical transmission of disease. Also, control function for minimising the cost of spraying and dropout is calculated. Numerical simulations have been established to find basic reproduction number and stability and minimising control function.