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A. K. Adamu, J. E. Ochigbo, B Williams and C. E. Okorie

**keywords:** Basic reproduction number,Jacobian matrix, malaria, next generation matrix

Malaria is one of the oldest diseases studied for a long time from all angles. Many infectious diseases including malaria are preventable, yet they remain endemic in many communities due to lack of proper, adequate and timely control policies. Strategies for controlling the spread of any infectious disease include a rapid reduction in both the infected populations (if a cure is available) as well as a rapid reduction in the susceptible class if a vaccine is available. For diseases like malaria where the development of a vaccine is underway, it therefore makes it seemingly possible to reduce the susceptible class through vaccination. In this paper, we have investigated and modify an SPITR mathematical model of Fekaduet al. for the transmission and control of malaria disease by incorporating parameters for vaccination and vector reduction and as well, determine the basic reproduction number of the model. We showed that the disease free equilibrium (DFE) state is locally asymptotically stable if Ro is less than and unstable if greater than unity. This shows that if Ro is less than 1, malaria can be controlled in the population.

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