Appraisal and Simulation on Codynamics of Pneumonia and Meningitis with Vaccination Intervention: From a Mathematical Model Perspective

Abstract

The membranes that encompass the brain and spinal cord become inflamed by the potentially fatal infectious disease called pneumococcal meningitis. Pneumonia and meningitis “coinfection” refers to the presence of both conditions in a single host. In this work, we accounted for the dynamics of pneumonia and meningitis coinfection in communities by erroneously using a compartment model to analyze and suggest management techniques to stakeholders. We have used the next generation matrix approach and derived the effective reproduction numbers. When the reproduction number is less than one, the constructed model yields a locally asymptotically stable disease-free equilibrium point. Additionally, we conducted a sensitivity analysis to determine how different factors affected the incidence and transmission rate, which revealed that both the pneumonia and meningitis transmission rates are extremely sensitive. The performance of our numerical simulation demonstrates that the endemic equilibrium point of the pneumonia and meningitis coinfection model is locally asymptotically stable when <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi mathvariant="normal">max</a:mi> <a:mfenced open="{" close="}"> <a:mrow> <a:mtext> </a:mtext> <a:msub> <a:mrow> <a:mi mathvariant="script">R</a:mi> </a:mrow> <a:mrow> <a:mn>1</a:mn> </a:mrow> </a:msub> <a:mo>,</a:mo> <a:msub> <a:mrow> <a:mi mathvariant="script">R</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> </a:mrow> </a:mfenced> <a:mo>&gt;</a:mo> <a:mn>1</a:mn> </a:math> . Finally, as preventative and control measures for the coinfection of pneumonia and meningitis illness, the stakeholders must concentrate on reducing the transmission rates, reducing vaccination wane rates, and boosting the portion of vaccination rates for both pneumonia and meningitis.