ABSTRACT
This chapter presents a new investigation of a non-integer order SIRS-SI model of malaria disease and examines the transmission of malaria in the human body. Malaria is a big life-threatening problem as per the data of WHO in 2017. Among 87 countries, there were approximate 219 million malaria cases that arose. According to WHO, approximately 435,000 people died from malaria in 2017. In this chapter, we discuss the SIRS-SI malaria model by employing the Atangana and Baleanu operator, which has a strong memory effect. We discuss the treatment of malaria and how to control it. To analyse the existence and uniqueness (EU) of the solution of the SIRS-SI model with a non-singular and non-local kernel, we applied the fixed-point theorem. It is shown that the treatments for malaria have an effective impact on human populations and mosquito populations. We obtain the numerical results of the SIRS-SI malaria disease model with a non-integer order by applying a new powerful technique called q-HATM. To demonstrate the various parameters on the treatment of malaria disease, we used the Maple package. The numerical outcome shows that for the arbitrary order SIRS-SI model of malaria disease, the discussed method is very strong, effective and computationally very easy.
