Browsing by Author "Mpolya, Emmanuel A."

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    Mathematical Modeling on the Spread of Awareness Information to Infant Vaccination
    (Applied Mathematics, 2015) Aminiel, Joram; Kajunguri, Damian; Mpolya, Emmanuel A.
    In this paper, we examine the importance of spreading awareness information about infant vaccination in a population. A mathematical model for the spread of infant vaccination awareness information is proposed and analyzed quantitatively using the stability theory of the differential equations. The basic reproduction number 𝑅0 is obtained and its sensitivity analysis is carried out. The awareness free equilibrium is also proved to be locally and globally stable. Consideration is taken when 𝑅0 is greater than unity, which indicates that infant vaccination awareness information will invade the population and cause immunization to succeed. It is also proved that the maximum awareness equilibrium is locally stable if 𝑅0 is greater than unity. Numerical results show that word-of-mouth has a more impact on infant vaccination as compared to mass media, but better results are obtained by a combination of both word-of-mouth and mass media. For a successful infant vaccination programme, there is a need to emphasize both forms of awarenes.
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    Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination
    (Applied and Computational Mathematics, 2015) Mpande, Leopard C.; Kajunguri, Damian; Mpolya, Emmanuel A.
    In this paper, a metapopulation model is formulated as a system of ordinary differential equations to study the impact of vaccination on the spread of measles. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if 1 C R < and unstable if 1 C R > . We show that when there are no movements between the two patches, there exists at least one endemic equilibrium for all 1 Ci R > and bifurcation analysis of endemic equilibrium point proves that forward (supercritical) bifurcation occurs in each patch. Numerical simulation results are also presented to validate analytical results and to show the impact of vaccination on the incidence and prevalence of measles in a metapopulation.