Dengue is a deadly illness in almost all parts of Indonesia, including East Java. This paper analyzes the dengue transmission model by considering the recruitment rate in the form of the logistic growth of the human population. The model parameters were estimated using least-squares methods based on dengue data in East Java, Indonesia. The model analysis results obtained two equilibria, namely the diseases-free and the endemic equilibria. The disease-free equilibrium is asymptotically stable if the basic reproduction number $R_0$ $<$ 1, while the endemic equilibrium is asymptotically stable if $R_0$ $>$ 1. The control variables were incorporated, and an optimal control problem was analyzed using the Pontryagin maximum principle. Finally, the cost-effectiveness analysis suggests that prevention only is the the most cost-effective strategy required to control dengue disease.

Both tuberculosis (TB) and COVID-19 are infectious diseases with similar clinical manifestations, which mainly affect the lungs. Clinical studies have revealed that the immunosuppressive drugs taken by COVID-19 patients can affect the immunological functions in the body, which can cause the patients to contract active TB via a new infection or reinfection, and the co-infection of the two diseases portends a clinical complexity in the management of the patients. Thus, this paper presents a mathematical model to study the dynamics and control of COVID-19-TB co-infection. The full model of the co-infection is split into two submodels, namely, the TB-only and the COVID-19-only models. The equilibria of the disease-free and endemic situations of the two sub-models are shown to be globally asymptotically stable when their control reproduction numbers $R_o^{TV},R_o^{CV}<1$ and ${\tilde{R}}_o^{TV},{\tilde{R}}_o^{CV}>1$, respectively. However, the disease-free equilibrium of the co-infection model was found to lose its global stability property when the reproduction number $R_o^F<1$, therefore exhibiting a backward bifurcation. Uncertainty and sensitivity analysis of the associated reproduction number of the full model has been performed by using the Latin hypercube sampling/Pearson rank correlation coefficient (LHS/PRCC) method. The rate of transmission of COVID-19 and the proportions of individuals vaccinated with Bacillus Calmette-Guérin (BCG) and against COVID-19 were found to be highly significant in the spread and control of COVID-19-TB co-infection. Furthermore, the simulation results show that decreasing the COVID-19 transmission rate and increasing the proportion of people vaccinated with BCG and against COVID-19 can lower the number of cases of COVID-19-TB co-infection. Therefore, measures to reduce the transmission rate and the provision of adequate resources to increase the proportions of people vaccinated against TB and COVID-19 should be implemented to minimize the cases of co-infection.