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

Abstract

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.

Figure 1

The map displays the locations and distributions of metropolitan and rural health districts in NSW Australia. (Source: https://www.health.nsw.gov.au/lhd/Documents/lhd-wall-map.pdf).

Figure 2

COVID-19 case counts and incidence rates (per one million population) in NSW metropolitan and rural areas (red bars indicate rural cases and blue bars indicate metropolitan cases) (Data source: https://www.health.nsw.gov.au/lhd/Pages/default.aspx).

Figure 3

The SEIR-X (SEMCNHRD) model structure: the population is divided into the following eight classes: susceptible, exposed (and not yet symptomatic), infectious (symptomatic) i.e. mild (mild or moderate symptom) and critical (severe symptom), death and recovered (i.e. isolation, recovered, or otherwise non-infectious).

Figure 4

Cumulative confirmed COVID-19 cases data from January 01, 2022 to February 10, 2022 (red dash) and the corresponding model best fit (blue solid curve) in NSW.

Figure 5

Correlation between Mild cases and the corresponding parameters of the model.

Figure 6

Correlation between Critical cases and the corresponding parameters of the model.

Figure 7

COVID-19 model sensitivities to its associated parameters of the model.

Figure 8

Contour plots of the basic reproduction number ${\mathrm{R}}_0$ with various values of other parameters.

Figure 9

Control profile for preventive strategy (${\mathrm{u}}_1(\mathrm{t}))$ and its effects on the COVID-19 dynamics in metropolitan health districts (left hand side) and rural health districts (right hand side).

Figure 9

Control profile for preventive strategy (${\mathrm{u}}_1(\mathrm{t}))$ and its effects on the COVID-19 dynamics in metropolitan health districts (left hand side) and rural health districts (right hand side).

Figure 10

Control profile for management strategy (${\mathrm{u}}_2(\mathrm{t}))$ and its effects on the COVID-19 dynamics in metropolitan health districts (left hand side) and rural health districts (right hand side).

Figure 10

Control profile for management strategy (${\mathrm{u}}_2(\mathrm{t}))$ and its effects on the COVID-19 dynamics in metropolitan health districts (left hand side) and rural health districts (right hand side).

Figure 11

Control profile for preventive (${\mathrm{u}}_1(\mathrm{t}))$ and management (${\mathrm{u}}_2(\mathrm{t}))$ strategies and its effects on the COVID-19 dynamics in metropolitan health districts (left hand side) and rural health districts (right hand side).

Figure 11

Control profile for preventive (${\mathrm{u}}_1(\mathrm{t}))$ and management (${\mathrm{u}}_2(\mathrm{t}))$ strategies and its effects on the COVID-19 dynamics in metropolitan health districts (left hand side) and rural health districts (right hand side).