2011 · 19 citations · 14 references
Veterinary MedicineChild HealthInfectious DiseasesEpidemiologyInfectious Disease EpidemiologyPediatric Infectious DiseasesInfant Infectious DiseasesInfectious Disease DynamicsInfectious Disease PreventionMalariaPopulation Dynamics ModelingTransmission DynamicsCerebral MalariaCo-infection DynamicsEndemic DynamicsEpidemic ModelsInfectious Disease ModelsMalaria Co-infectionMathematical Modeling Of EpidemicsReproduction Number Analysis
Disease and poverty are a major threat to child survival in the developing world, where access to good nutrition, sanitation and health care is poor. In this paper, a mathematical model for malaria and meningitis co-infection among children under five years of age is developed and analysed. We establish the basic reproduction number Rmm for the model, which is a measure of the course of the co-infection. The analysis shows that the disease-free equilibrium of the model may not be globally asymptotically stable whenever Rmm is less than unity. The Centre Manifold theorem is used to show that the model has a unique endemic equilibrium which is locally asymptotically stable when Rmm 1. We deduce further that a reduction in malaria infection cases either through protection or prompt effective treatment, which is dependent on the socio-economic status of a community, would reduce the number of new co-infection cases.
14
Ordinary Differential Equations.
C. E. Langenhop, G. Birkhoff, G.-C Rota · American Mathematical Monthly · 1963 · 1.3K citations