Impacts of optimal control strategies on the HBV and COVID-19 co-epidemic spreading dynamics

Abstract

Different cross-sectional and clinical research studies investigated that chronic HBV infected individuals' co-epidemic with COVID-19 infection will have more complicated liver infection than HBV infected individuals in the absence of COVID-19 infection. The main objective of this study is to investigate the optimal impacts of four time dependent control strategies on the HBV and COVID-19 co-epidemic transmission using compartmental modeling approach. The qualitative analyses of the model investigated the model solutions non-negativity and boundedness, calculated all the models effective reproduction numbers by applying the next generation operator approach, computed all the models disease-free equilibrium point (s) and endemic equilibrium point (s) and proved their local stability, shown the phenomenon of backward bifurcation by applying the Center Manifold criteria. By applied the Pontryagin's Maximum principle, the study re-formulated and analyzed the co-epidemic model optimal control problem by incorporating four time dependent controlling variables. The study also carried out numerical simulations to verify the model qualitative results and to investigate the optimal impacts of the proposed optimal control strategies. The main finding of the study reveals that implementation of protections, COVID-19 vaccine, and treatment strategies simultaneously is the most effective optimal control strategy to tackle the HBV and COVID-19 co-epidemic spreading in the community.

Keywords: COVID-19; Co-epidemic; HBV; Optimal control measures; Protection; Vaccination.

Figure 1

The COVID-19 and HBV co-epidemic individuals flow diagram where the functions λ_H(t) and λ_C(t) are described in Eqs. (1) and (2) respectively.

Figure 2

Behaviors of the dynamical system (3) solutions at ${\mathcal{R}}_{\text{HC}}=2.68>1.$.

Figure 3

Impact single strategies on the total number of HBV and COVID-19 co-epidemic population.

Figure 4

Impacts of double strategies on the number of HBV and COVID-19 co-epidemic population.

Figure 5

Impacts of triple strategies on the number of HBV and COVID-19 co-epidemic population.

Figure 6

Simulation of total population $(I_{\mathit{AC}}+I_{\mathit{CC}})$ with all controlling strategies.