Mohammad Ghani, Yolanda Norasia, Wahyuni Ningsih
The dynamics of CoVid-19 disease becomes a concern in this paper. Initially, the positivity and boundedness are established to ensure that the number of susceptible, infected, quarantined, and recovered individuals are always positive in the population and the population numbers are always bounded. The equilibrium points of disease-free and endemic are then determined for uncontrolled dynamical system. Based on the equilibrium points, we can provide the basic reproduction number to ensure that infectious disease can transmit or not in the population. The infection has ability to transmit in the population if R0>1 and vice versa. The local stability is established through the Jacobian matrix at the disease-free and endemic equilibrium points. The appropriate Lyapunov function is initially introduced to provide the global stability of dynamical system. Moreover, the sensitivity analysis is used to determine the dominant parameters for each state variable (most positive or negative). The least square technique is used to compare the numerical results using the fourth-order Runge–Kutta and actual data of CoVid-19 disease in Semarang, Indonesia. Moreover, Continuous Time Markov Chain (CTMC) gives the same patterns between the deterministic and stochastic results. Because vaccination and social distancing have a significant impact on the profile of susceptible, infected, quarantined, and recovered classes, then we introduce a mathematical model of CoVid-19 with two time-dependent controls (u1,u2)(t). It follows from the results obtained, the implementation of control gives the number of infected, quarantined, and recovered individuals decreased, and the number of susceptible individuals increased. The neural network approach also gives the significant estimations based on the root mean square error by using the training function of Levenberg-Marquadt. © Foundation for Scientific Research and Technological Innovation 2023.
Faculty of Advanced Technology and Multidiscipline, Universitas Airlangga, Surabaya, 60115, Indonesia; Department of Mathematics, Universitas Islam Negeri Walisongo, Semarang, 50185, Indonesia; Department of Chemical Engineering, Politeknik Negeri Malang, Malang, 65141, Indonesia