Industrial Mathematics
Permanent URI for this collectionhttp://197.211.34.35:4000/handle/123456789/189
Industrial Mathematics
Browse
Item Mathematical Model of COVID-19 Pandemic with Double Dose Vaccination(Springer Science and Business Media LLC, 2023-03-06) Olumuyiwa James Peter; Hasan S. Panigoro; Afeez Abidemi; Mayowa M. Ojo; Festus Abiodun OguntoluThis paper is concerned with the formulation and analysis of an epidemic model of COVID-19 governed by an eight-dimensional system of ordinary differential equations, by taking into account the first dose and the second dose of vaccinated individuals in the population. The developed model is analyzed and the threshold quantity known as the control reproduction number is obtained. We investigate the equilibrium stability of the system, and the COVID-free equilibrium is said to be locally asymptotically stable when the control reproduction number is less than unity, and unstable otherwise. Using the least-squares method, the model is calibrated based on the cumulative number of COVID-19 reported cases and available information about the mass vaccine administration in Malaysia between the 24th of February 2021 and February 2022. Following the model fitting and estimation of the parameter values, a global sensitivity analysis was performed by using the Partial Rank Correlation Coefficient (PRCC) to determine the most influential parameters on the threshold quantities. The result shows that the effective transmission rate, the rate of first vaccine dose, the second dose vaccination rate and the recovery rate due to the second dose of vaccination are the most influential of all the model parameters. We further investigate the impact of these parameters by performing a numerical simulation on the developed COVID-19 model. The result of the study shows that adhering to the preventive measures has a huge impact on reducing the spread of the disease in the population. Particularly, an increase in both the first and second dose vaccination rates reduces the number of infected individuals, thus reducing the disease burden in the population.Item Modelling the impacts of media campaign and double dose vaccination in controlling COVID-19 in Nigeria(Elsevier BV, 2023-10) N.I. Akinwande; S.A. Somma; R.O. Olayiwola; T.T. Ashezua; R.I. Gweryina; F.A. Oguntolu; O.N. Abdurahman; F.S. Kaduna; T.P. Adajime; F.A. Kuta; S. Abdulrahman; A.I. Enagi; G.A. Bolarin; M.D. Shehu; A. UsmanCorona virus disease (COVID-19) is a lethal disease that poses public health challenge in both developed and developing countries of the world. Owing to the recent ongoing clinical use of COVID-19 vaccines and non-compliance to COVID-19 health protocols, this study presents a deterministic model with an optimal control problem for assessing the community-level impact of media campaign and double-dose vaccination on the transmission and control of COVID-19. Detailed analysis of the model shows that, using the Lyapunov function theory and the theory of centre manifold, the dynamics of the model is determined essentially by the control reproduction number (Rmv). Consequently, the model undergoes the phenomenon of forward bifurcation in the absence of the double dose vaccination effects, where the global disease-free equilibrium is obtained whenever Rmv≤1. Numerical simulations of the model using data relevant to the transmission dynamics of the disease in Nigeria, show that, certain values of the basic reproduction number ((R0≥7)) may not prevent the spread of the pandemic even if 100% media compliance is achieved. Nevertheless, with assumed 75% (at R0=4)) media efficacy of double dose vaccination, the community herd immunity to the disease can be attained. Furthermore, Pontryagin's maximum principle was used for the analysis of the optimized model by which necessary conditions for optimal controls were obtained. In addition, the optimal simulation results reveal that, for situations where the cost of implementing the controls (media campaign and double dose vaccination) considered in this study is low, allocating resources to media campaign-only strategy is more effective than allocating them to a first-dose vaccination strategy. More so, as expected, the combined media campaign-double dose vaccination strategy yields a higher population-level impact than the media campaign-only strategy, double-dose vaccination strategy or media campaign-first dose vaccination strategy.