This study presents a deterministic mathematical model of monkeypox disease transmission dynamics with an age‐structured human population divided into two subgroups of children (Group 1) and adults (Group 2). Two equilibrium points, monkeypox‐free, E⁰, and a unique monkeypox‐endemic equilibrium point, E¹, are established. The age‐structured monkeypox basic reproduction number, ℝ₀, is computed using the next‐generation matrix approach and established to be ℝ₀ = 1.2448. The Lyapunov functions are constructed; together with LaSalle’s invariance principle, the monkeypox‐free equilibrium point, E⁰, is established to be globally asymptotically stable whenever ℝ₀ ≤ 1, as confirmed by the Lyapunov stability method, and the monkeypox‐endemic equilibrium point, E¹, is globally asymptotically stable whenever ℝ₀ > 1. Sensitivity analysis of the threshold quantity ℝ₀ is performed using the Latin hypercube sampling method and Pearson’s partial rank correlation coefficient, and the results showed that the parameters β₁₁, β₂₂, μ, ν₁, Λ₁, ν₂ were the most sensitive to the spread of monkeypox infection in an age‐structured population. It is, therefore, suggested that the rate of monkeypox infection can be reduced by ensuring that the rate of interaction between susceptible children and infected children and between susceptible adults and infected adults is minimized. Moreover, the spread of monkeypox infection can be curbed by emphasizing controls such as early diagnosis and treatment and hospitalization of critically ill infectives.

This study presents a novel mathematical model that captures the co-dynamics of pulmonary tuberculosis in the presence of opportunistic pneumonia. The model integrates opportunistic pneumonia into the classical pulmonary tuberculosis transmission framework, based on clinical evidence of a lethal synergism between the two diseases. A Holling-type saturation function is utilized to reflect the impact of natural immunity on the progression from latent tuberculosis infection to active disease. Asymptomatic infectious individuals can transmit the infection unnoticed, thereby significantly contributing to the high rate of transmission. Thus, the screening of asymptomatic individuals is incorporated into the model as a strategy to mitigate the prevalence of co-infections. A comprehensive sensitivity analysis and numerical simulations were conducted to evaluate the effects of various interventions, including enhancing natural immunity, screening asymptomatic and latently infected individuals, improving vaccine efficacy, and treating patients with severe pulmonary tuberculosis. The sensitivity analysis reveals that improving vaccine efficacy is the most effective strategy for minimizing co-infections. Simulations also demonstrate that increased screening and treatment rates significantly reduce the burden of pulmonary tuberculosis-pneumonia co-infections. These results underscore the need to develop vaccines with higher efficacy to reduce co-infections of pulmonary tuberculosis and opportunistic pneumonia. Additionally, the study recommends expanded screening of asymptomatic tuberculosis cases and the strengthening of immunity among latently infected populations.

In this paper, a deterministic mathematical model illustrating the transmission dynamics of pulmonary tuberculosis and pneumonia co-infection is formulated, incorporating a drug-resistant strain. The model employs a Holling-type functional response to capture the impact of natural immunity on the progression from latent tuberculosis infection to active disease, as well as its role in controlling drug-resistant pulmonary tuberculosis-pneumonia co-infections. The model is extended to include optimal control theory, aimed at identifying strategies to minimize co-infections using prevention, screening of latently infected individuals, and treatment as control variables. Pontryagin’s Maximum Principle is applied to characterize the optimal control system. The resulting optimality system is then solved numerically using the Runge-Kutta-based forward-backward sweep method. Numerical simulations demonstrate that enhancing natural immunity among latently infected individuals significantly reduces the number of co-infected cases. The optimal control analysis indicates that the most effective strategy for controlling or reducing co-infections of drug-resistant tuberculosis and pneumonia is the combined optimization of infection prevention and screening of latently infected individuals. These findings underscore the importance of scaling up preventive measures against pulmonary tuberculosis and opportunistic pneumonia, alongside screening efforts, to effectively control co-infections. Additionally, the study recommends strengthening immunity among latently infected populations to further reduce the prevalence of co-infections.