Mathematical model analysis and numerical simulation for codynamics of meningitis and pneumonia infection with intervention

Abstract

In this paper, we have considered a deterministic mathematical model to analyze effective interventions for meningitis and pneumonia coinfection as well as to make a rational recommendation to public healthy, policy or decision makers and programs implementers. We have introduced the epidemiology of infectious diseases, the epidemiology of meningitis, the epidemiology of pneumonia, and the epidemiology of infection of meningitis and pneumonia. The positivity and boundedness of the sated model was shown. Our model elucidate that, the disease free equilibrium points of each model are locally asymptotically stable if the corresponding reproduction numbers are less than one and globally asymptotically stable if the corresponding reproduction numbers are greater than one. Additionally, we have analyzed the existence and uniqueness of the endemic equilibrium point of each sub models, local stability and global stability of the endemic equilibrium points for each model. By using standard values of parameters we have obtained from different studies, we found that the effective reproduction numbers of meningitis $${\mathcal{R}}_{eff(m)}=9$$ R e f f ( m ) = 9 and effective reproduction numbers of pneumonia $${\mathcal{R}}_{eff(p)}=11$$ R e f f ( p ) = 11 that lead us to the effective reproduction number of the meningitis and pneumonia co-infected model is $$max\left\{ {\mathcal{R}}_{eff\left(m\right)}, {\mathcal{R}}_{eff(p)} \right\}=9$$ m a x R e f f m , R e f f ( p ) = 9 . Applying sensitivity analysis, we identified the most influential parameters that can change the behavior of the solution of the meningitis pneumonia coinfection dynamical system are $${\alpha }_{1} , {\alpha }_{2}$$ α 1 , α 2 and $$\pi$$ π . Biologically, decrease in $${\alpha }_{1}$$ α 1 and increasing in $$\pi$$ π is a possible intervention strategy to reduce the infectious from communities. Finally, our numerical simulation has shown that vaccination against those diseases, reducing contact with infectious persons and treatment have the great effect on reduction of these silent killer diseases from the communities.

Mathematical model analysis of effective intervention strategies on transmission dynamics of hepatitis B virus

“…In recent years, mathematical and statistical models of infectious diseases have provided useful insights into the dynamics and control of infectious disease transmission 17 . A mathematical model of the dynamics of disease transmission is needed to provide better insight into disease behavior, optimize the use of limited resources, and recommend infectious disease control approaches 18 . A mathematical model of the infectivity dynamics of each disease is essential to gain better insight into disease behavior.…”

Mathematical Modeling Investigation of Violence and Racism Coexistence as a Contagious Disease Dynamics in a Community

“…It can be considered as mind infection, and its expansion and impact on individuals indicted similar to infectious diseases, like tuberculosis (TB), COVID-19, and pneumonia pathogenic agents [5]. Various social science studies related to individual behaviors such as violence, racism, social media addiction, and corruption have been carried out by many scholars throughout the world [6][7][8][9][10][11][12][13][14][15]. Violence and violation are crucially at the heart of racism, and hence, in principle, the coexistence of violence and racism on individuals in a community is assured [14].…”

“…Mathematical modeling has a continuous fundamental role in understanding of the various aspects of dynamical system of real-world situations like [ 17 – 21 ]. It has been formulated and analyzed in different disciplines such as natural sciences as well as social science like [ 1 – 5 , 9 , 22 – 33 ]. Many researchers have applied infectious disease dynamics model to violence, racism, social media addition, corruption, and other social situations.…”

The Impact of Protection Measures and Treatment on Pneumonia Infection: A Mathematical Model Analysis supported by Numerical Simulation

“…Communicable diseases are clinically evident illnesses caused by microorganisms and among them; those that most common worldwide causes of death include lower respiratory infections (such as pneumonia) and HIV [12, 16, 23]. Global Burden of Diseases (GBD), 2019 study reported that lower respiratory tract infections (LRTI) including pneumonia and bronchiolitis impacted 489 million individuals in our world [21].…”

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