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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 and numerical simulation for codynamics of meningitis and pneumonia infection with intervention