Mathematical analysis of a two-strain tuberculosis model in Bangladesh

Modelling COVID-19 pandemic control strategies in metropolitan and rural health districts in New South Wales, Australia

COVID-19 remains a significant public health problem in New South Wales, Australia. Although the NSW government is employing various control policies, more specific and compelling interventions are needed to control the spread of COVID-19. This paper presents a modified SEIR-X model based on a nonlinear ordinary differential equations system that considers the transmission routes from asymptomatic (Exposed) and symptomatic (Mild and Critical) individuals. The model is fitted to the corresponding cumulative number of cases in metropolitan and rural health districts of NSW reported by the Health Department and parameterised using the least-squares method. The basic reproduction number [Formula: see text], which measures the possible spread of COVID-19 in a population, is computed using the next generation operator method. Sensitivity analysis of the model parameters reveals that the transmission rate had an enormous influence on [Formula: see text], which may be an option for controlling this disease. Two time-dependent control strategies, namely preventive (it refers to effort at inhibiting the virus transmission and prevention of case development from Exposed, Mild, Critical, Non-hospitalised and Hospitalised population) and management (it refers to enhance the management of Non-hospitalised and Hospitalised individuals who are infected by COVID-19) measures, are considered to mitigate this disease's dynamics using Pontryagin's maximum principle. The most sensible control strategy is determined through the cost-effectiveness analysis for the metropolitan and rural health districts of NSW. Our findings suggest that of the single intervention strategies, enhanced preventive strategy is more cost-effective than management control strategy, as it promptly reduces COVID-19 cases in NSW. In addition, combining preventive and management interventions simultaneously is found to be the most cost-effective. Alternative policies can be implemented to control COVID-19 depending on the policymakers' decisions. Numerical simulations of the overall system are performed to demonstrate the theoretical outcomes.

Variance-based sensitivity analysis of tuberculosis transmission models

Mathematical models are widely used to provide evidence to inform policies for tuberculosis (TB) control. These models contain many sources of input uncertainty including the choice of model structure, parameter values and input data. Quantifying the role of these different sources of input uncertainty on the model outputs is important for understanding model dynamics and improving evidence for policy making. In this paper, we applied the Sobol sensitivity analysis method to a TB transmission model used to simulate the effects of a hypothetical population-wide screening strategy. We demonstrated how the method can be used to quantify the importance of both model parameters and model structure and how the analysis can be conducted on groups of inputs. Uncertainty in the model outputs was dominated by uncertainty in the intervention parameters. The important inputs were context dependent, depending on the setting, time horizon and outcome measure considered. In particular, the choice of model structure had an increasing effect on output uncertainty in high TB incidence settings. Grouping inputs identified the same influential inputs. Wider use of the Sobol method could inform ongoing development of infectious disease models and improve the use of modelling evidence in decision making.