Mathematical assessment of the role of denial on COVID-19 transmission with non-linear incidence and treatment functions
Reuben Iortyer Gweryina, Chinwendu E. Madubueze, Francis Shienbee Kaduna
Abstract
A mathematical model describing the dynamics of Corona virus disease 2019 (COVID-19) is constructed and studied. The model assessed the role of denial on the spread of the pandemic in the world. Dynamic stability analyzes show that the equilibria, disease-free equilibrium (DFE) and endemic equilibrium point (EEP) of the model are globally asymptotically stable for R0<1 and R0>1, respectively. Again, the model is shown via numerical simulations to possess the backward bifurcation, where a stable DFE co-exists with one or more stable endemic equilibria when the control reproduction number, R0 is less than unity and the rate of denial of COVID-19 is above its upper bound. We then apply the optimal control strategy for controlling the spread of the disease using the controllable variables such as COVID-19 prevention, hospitalization and maximum treatment efforts. Using the Pontryagin maximum principle, we derive analytically the optimal controls of the model. The aforementioned control strategies are performed numerically in the presence of denial and without denial rate. Among such experiments, results without denial have shown to be more productive in ending the pandemic than others where the denial of the disease invalidates the effectiveness of the controls causing the disease to continue ravaging the globe.