Media campaigns, early diagnosis, isolation and treatment on bacterial meningitis outbreak prevention: A modeling study

Abstract

Bacterial meningitis is a severe infection affecting the protective membranes of the brain and spinal cord, with rapidly worsening symptoms that can lead to life-threatening complications. This study presents an autonomous deterministic epidemic model, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>S</mml:mi> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mi>M</mml:mi> <mml:mi>R</mml:mi> <mml:mi>S</mml:mi> </mml:math> , to explore the dynamics of bacterial meningitis in a community implementing control strategies like media coverage, early diagnosis, isolation, and treatment. We adjust the transmission probability based on media coverage and calculate the effective reproduction number, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> </mml:math> , which includes contributions from asymptomatic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="script">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:mi>a</mml:mi> </mml:msubsup> </mml:math> and symptomatic individuals <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="script">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> </mml:msubsup> </mml:math> . We derive the basic reproduction number, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">R</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msub> </mml:math> , to characterize initial infection spread and analyze the local stability of infection-free and endemic equilibria, using the Routh-Hurwitz criteria. For global stability, we apply Castillo-Chavez method for the infection-free equilibrium and the Lyapunov functional technique for the endemic equilibrium, after a uniform persistence study. A local sensitivity analysis evaluates the impact of each parameter on the threshold dynamical parameters <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="script">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:mi>a</mml:mi> </mml:msubsup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="script">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> </mml:msubsup> </mml:math> . We also explore an optimal control problem using Pontryagin's maximum principle. The paper concludes with numerical simulations that bridge theoretical and numerical findings.