Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures.

Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures. Comput Math Methods Med. 2018;2018:2657461 Authors: Asamoah JKK, Nyabadza F, Seidu B, Chand M, Dutta H Abstract Vaccination and treatment are the most effective ways of controlling the transmission of most infectious diseases. While vaccination helps susceptible individuals to build either a long-term immunity or short-term immunity, treatment reduces the number of disease-induced deaths and the number of infectious individuals in a community/nation. In this paper, a nonlinear deterministic model with time-dependent controls has been proposed to describe the dynamics of bacterial meningitis in a population. The model is shown to exhibit a unique globally asymptotically stable disease-free equilibrium ℰ0, when the effective reproduction number ℛVT ≤ 1, and a globally asymptotically stable endemic equilibrium ℰ1, when ℛVT > 1; and it exhibits a transcritical bifurcation at ℛVT = 1. Carriers have been shown (by Tornado plot) to have a higher chance of spreading the infection than those with clinical symptoms who will sometimes be bound to bed during the acute phase of the infection. In order to find the best strategy for minimizing the number of carriers and ill individuals and the cost of control implementation, an optimal control problem is set up by defining a Lagrangian function L to be minimized subject to the proposed model. ...
Source: Computational and Mathematical Methods in Medicine - Category: Statistics Tags: Comput Math Methods Med Source Type: research