Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures

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. Numerical simulation of the optimal problem demonstrates that the best strategy to control bacterial meningitis is to combine vaccination with other interventions (such as treatment and public health education). Additionally, this research suggests that stakeholders should press hard for the production of existing/new vaccines and antibiotics and their disbursement to areas that are most affected by bacterial meningitis, especially Sub-Saharan Africa; furthermore, individuals who live in communities where the environment is relatively warm (hot/moisture) are advised to go for vaccination against bacterial meningitis.

Stability Analysis of Mathematical Models of the Dynamics of Spread of Meningitis with the Effects of Vaccination, Campaigns and Treatment

“…Hampir semua bakteri yang masuk ke meninges dapat menyebabkan meningitis. Meningitis bakteri umumnya disebabkan oleh tiga bakteri yaitu Neisseria meningitidis, Haemophilus influenzae, dan Streptococcus pneumoniae [6]. Meningitis bakteri hanya ditemukan pada manusia dan ditularkan dari satu orang ke orang lain [7].…”

Modeling co-dynamics of pneumonia and meningitis diseases

“…dt from (2) into (8) and collecting all positive terms together and also negative terms together, we obtain…”

“…Several scholars have developed different models to study the dynamics of different epidemic diseases. Some of them [7,8] proposed a mathematical model of pneumonia and meningitis; moreover, [9] investigated the co-dynamics of pneumonia and typhoid fever diseases with optimal control and cost-effectiveness analysis. The result of the study revealed that prevention of typhoid fever and treatment of pneumonia is the most cost-effective strategies from the proposed ones.…”

Stability Analysis of Mathematical Model of Meningococcal Meningitis Disease Between Two Regions Using (Scir)ina-(Si)ksa Compartment

“…Meningitis vaccine contains antigens, a substance that stimulates the immune system to form antibodies and fight the bacteria that cause meningitis, hence vaccine can reduce the risk of meningococcal Meningitis disease. Mathematics research about meningitis vaccine using control had done by Asamoah, et al (2018). Blyuss (2016) also had discussed temporary population immunity to meningitis disease which can be useful to measure the efficiency of vaccines.…”

“…The incubation period of meningococcal disease is 3 to 4 days, with a range of 2 to 10 days. Meningitis is the most common presentation of invasive meningococcal infection (meningococcal disease) and results from hematogenous dissemination of the organism (Asamoah, et al 2018). So, time unit (t) is assumed to be calculated in weeks because the incubation period may exceed seven days (one week).…”