Abstract :
In this paper, we proposed a deterministic model of pneumonia-meningitis coinfection. We used a system of seven ordinary
differential equations. Firstly, the qualitative behaviours of the model such as positivity of the solution, existence of the solution,
the equilibrium points, basic reproduction number, analysis of equilibrium points, and sensitivity analysis are studied. The
disease-free equilibrium is locally asymptotically stable if the basic reproduction number is kept less than unity, and conditions for
global stability are established. Then, the basic model is extended to optimal control by incorporating four control interventions,
such as prevention of pneumonia as well as meningitis and also treatment of pneumonia and meningitis diseases. The optimality
system is obtained by using Pontryagin’s maximum principle. For simulation of the optimality system, we proposed five strategies
to check the effect of the controls. First, we consider prevention only for both diseases, and the result shows that applying
prevention control has a great impact in bringing down the expansion of pneumonia, meningitis, and their coinfection in the
specified period of time. 'e other strategies are prevention effort for pneumonia and treatment effort for meningitis, prevention
effort for meningitis and treatment effort for pneumonia, treatment effort for both diseases, and using all interventions. We
obtained that each of the listed strategies is effective in minimizing the expansion of pneumonia-only, meningitis-only, and
coinfectious population in the specified period of time.
