Stability and global sensitivity analysis of the transmission dynamics of malaria with relapse and ignorant infected humans

In this paper we present a more realistic mathematical model for the transmission dynamics of malaria by extending the classical SEIRS scheme and the model of Hai-Feng Huo and Guang-Ming Qiu [21] by adding the ignorant infected humans compartment. We analyze the global asymptotically stabilities of the model by the use of the basic reproduction number R_0 and we prove that when R_0≦1, the disease-free equilibrium is globally asymptotically stable. That is malaria dies out in the population. When R_0>1, there exists a co-existing unique endemic equilibrium which is globally asymptotically stable. The global sensitivity analysis have been done through the partial rank correlation coefficient using the samples generated by the use of latin hypercube sampling method and shows that the most influence parameters in the spread of malaria are the proportion θ of infectious humans who recover and the recovery rate γ of infectious humans. In order to eradicate malaria, we have to decrease the number of ignorant infected humans by testing peoples and treat them. Numerical simulations show that malaria can be also controlled or eradicated by increasing the recovery rate γ of infectious humans, decreasing the number of ignorant infected humans and decreasing the average number n of mosquito bites.