Sensitivity assessment and optimal economic evaluation of a new COVID-19 compartmental epidemic model with control interventions

Abstract

Optimal economic evaluation is pivotal in prioritising the implementation of non-pharmaceutical and pharmaceutical interventions in the control of diseases. Governments, decision-makers and policy-makers broadly need information about the effectiveness of a control intervention concerning its cost-benefit to evaluate whether a control intervention offers the best value for money. The outbreak of COVID-19 in December 2019, and the eventual spread to other parts of the world, have pushed governments and health authorities to take drastic socioeconomic, sociocultural and sociopolitical measures to curb the spread of the virus, SARS-CoV-2. To help policy-makers, health authorities and governments, we propose a Susceptible, Exposed, Asymptomatic, Quarantined asymptomatic, Severely infected, Hospitalized, Recovered, Recovered asymptomatic, Deceased, and Protective susceptible (individuals who observe health protocols) compartmental structure to describe the dynamics of COVID-19. We fit the model to real data from Ghana and Egypt to estimate model parameters using standard incidence rate. Projections for disease control and sensitivity analysis are presented using MATLAB. We noticed that multiple peaks (waves) of COVID-19 for Ghana and Egypt can be prevented if stringent health protocols are implemented for a long time and/or the reluctant behaviour on the use of protective equipment by individuals are minimized. The sensitivity analysis suggests that: the rate of diagnoses and testing, the rate of quarantine through doubling enhanced contact tracing, adhering to physical distancing, adhering to wearing of nose masks, sanitizing-washing hands, media education remains the most effective measures in reducing the control reproduction number $R_c,$ to less than unity in the absence of vaccines and therapeutic drugs in Ghana and Egypt. Optimal control and cost-effectiveness analysis are rigorously studied. The main finding is that having two controls (transmission reduction and case isolation) is better than having one control, but is economically expensive. In case only one control is affordable, then transmission reduction is better than case isolation. Hopefully, the results of this research should help policy-makers when dealing with multiple waves of COVID-19.

Keywords: COVID-19 model; Cost-effectiveness analysis; Hospitalization; Mathematical epidemiology; Optimal control analysis; Quarantine.

Fig. 1

Confirmed statistics of cumulative and daily cases in Egypt and Ghana as at November 10, 2020.

Fig. 2

Prototypical patterns of the model formulation.

Fig. 3

An epidemic model without birth/deaths, the disease always dies out, irrespective of Theorem 2.1 and Theorem 2.2.

Fig. 4

Predictive logistic model fit for COVID-19 reflecting real data from Ghana and Egypt taken from . Red: fast growth phase, yellow: transition to steady-state phase, green: ending phase .

Fig. 5

Number of cases per day.

Fig. 6

Model fitting of COVID-19 data to $SEA{I}_{s}H{R}^{A}RD{S}_p$ epidemic model from March 12, 2020 to May 31, 2020 for Ghana, and February 14, 2020 to May 31, 2020 for Egypt.

Fig. 7

Model fitting of COVID-19 data to $SEA{I}_{s}H{R}^{A}RD{S}_p$ epidemic model from July 1, 2020, to October 31, 2020, for Ghana, and Egypt.

Fig. 8

Model-predicted time series of the number of infected cases and recoveries.

Fig. 9

Time series forecast plot for Ghana, with an increase in reluctant behaviour on the use of protective equipment.

Fig. 10

PRCC plots for parameters in ${\mathcal{R}}_c$.

Fig. 11

Effect of varying the impact of $(1-{\beta }_1)$ health protocols.

Fig. 12

The dynamical effect of timely diagnoses and effective quarantine.

Fig. 13

Effect of varying the values of the transmission rate, $\beta ,$ and the transmissibility rate of the exposed class, ${\eta }_0$.

Fig. 14

Effect of varying the values of transmission rate, $\beta ,$ and transmissibility rate of the exposed class, ${\eta }_0$.

Fig. 15

Optimal simulation with the implementation of various control strategies for Egypt.

Fig. 16

Optimal simulation with the implementation of various control strategies for Ghana.

Fig. 17

Optimal simulation with the implementation of various control strategies for Egypt and Ghana.

Fig. 18

Infection Averted Ratio (IAR) results for Strategies A–C.

Fig. 19

Average cost-effectiveness ratio (ACER) results for Strategies A–C.