In this study we have develop a basic deterministic mathematical model to investigate SEIR Model and Simulation for controlling malaria Diseases Transmission without Intervention Strategies. The model has seven non-linear differential equations which describe the spread of malaria with three state variables for mosquitoes populations and four state variables for humans population and to introduce the model without intervention strategies. The models are analyzed qualitatively to determine criteria for control of a malaria transmission, and are used to calculate the basic reproduction R_0. The equilibria of malaria models are determined. In addition to having a disease-free equilibrium, which is locally asymptotically stable when the R_0<1, the basic malaria model manifest one's possession of (a quality of) the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists(at the same time) with a stable endemic equilibrium for a certain range of associated reproduction number less than one. The results also designing the effects of some model parameters, the infection rate and biting rate. The numerical analysis and numerical simulation results of the model suggested that the most effective strategies for controlling or eradicating the spread of malaria were suggest to use insecticide treated bed nets, indoor residual spraying, prompt effective diagnosis and treatment of infected individuals.
Malaria, Basic reproduction number, Stability analysis, Existence of Backward bifurcation analysis, Endemic equilibrium point
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