The success of mass vaccination campaigns may be jeopardized by human risky behaviors. For example, high level of vaccination coverage may induce early relaxation of social distancing. In this paper, we focus on the mutual influence between the decline in prevalence, due to the rise in the overall immunization coverage, and the consequent decrease in the compliance to social distancing measures. We consider an epidemic model where both the vaccination rate and the disease transmission rate are influenced by human behavior, which in turn depends on the current and past information about the spread of the disease. We highlight the impact of the information-related parameters on the transient and asymptotic behavior of the system that is on the early stage of the epidemic and its final outcome. Among the main results, we evidence that sustained oscillations may be triggered by the behavioral memory in the prevalence-dependent vaccination rate. However, the relaxation of social distancing may induce a switch from a cyclic regime to damped oscillations.
In this paper, we consider a mathematical model of COVID-19 transmission with vaccination where the total population was subdivided into nine disjoint compartments, namely, Susceptible(S), Vaccinated with the first dose(V1), Vaccinated with the second dose(V2), Exposed (E), Asymptomatic infectious (I), Symptomatic infectious (I), Quarantine (Q), Hospitalized (H) and Recovered (R). We computed a reproduction parameter, Rv, using the next generation matrix. Analytical and numerical approach is used to investigate the results. In the analytical study of the model: we showed the local and global stability of disease-free equilibrium, the existence of the endemic equilibrium and its local stability, positivity of the solution, invariant region of the solution, transcritical bifurcation of equilibrium and conducted sensitivity analysis of the model. From these analysis, we found that the disease-free equilibrium is globally asymptotically stable for Rv < 1 and unstable for Rv > 1. A locally stable endemic equilibrium exists for Rv > 1, which shows persistence of the disease if the reproduction parameter is greater than unity. The model is fitted to cumulative daily infected cases and vaccinated individuals data of Ethiopia from May 01, 2021 to January 31, 2022. The unknown parameters are estimated using the least square method with built-in MATLAB function 'lsqcurvefit'. Finally, we performed different simulations using MATLAB and predicted the vaccine dose that will be administered at the end of two years. From the simulation results, we found that it is important to reduce the transmission rate, infectivity factor of asymptomatic cases and increase the vaccination rate, quarantine rate to control the disease transmission. Predictions show that the vaccination rate has to be increased from the current rate to achieve a reasonable vaccination coverage in the next two years.
Mathematical modelling is important for better understanding of disease dynamics and developing strategies to manage rapidly spreading infectious diseases. In this work, we consider a mathematical model of COVID-19 transmission with double-dose vaccination strategy to control the disease. For the analytical analysis purpose, we divided the model into two parts: model with vaccination and without vaccination. Analytical and numerical approach is employed to investigate the results. In the analytical study of the model, we have shown the local and global stability of disease-free equilibrium, existence of the endemic equilibrium and its local stability, positivity of the solution, invariant region of the solution, transcritical bifurcation of equilibrium, and sensitivity analysis of the model is conducted. From these analyses, for the full model (model with vaccination), we found that the disease-free equilibrium is globally asymptotically stable for R v < 1 and is unstable for R v > 1 . A locally stable endemic equilibrium exists for R v > 1 , which shows the persistence of the disease if the reproduction parameter is greater than unity. The model is fitted to cumulative daily infected cases and vaccinated individuals data of Ethiopia from May 1, 2021 to January 31 , 2022 . The unknown parameters are estimated using the least square method with the MATLAB built-in function “lsqcurvefit.” The basic reproduction number R 0 and controlled reproduction number R v are calculated to be R 0 = 1.17 and R v = 1.15 , respectively. Finally, we performed different simulations using MATLAB. From the simulation results, we found that it is important to reduce the transmission rate and infectivity factor of asymptomatic cases and increase the vaccination coverage and quarantine rate to control the disease transmission.
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