ABSTRACT
In this manuscript, we have studied the dynamical behavior of a deadly COVID‐19 pandemic which has caused frustration in the human community. For this study, a new deterministic SEIHR fractional model is developed for the first time. The purpose is to perform a complete mathematical analysis and the design of an optimal control strategy for the proposed Caputo–Fabrizio fractional model. We have proved the existence and uniqueness of solutions by employing principle of mathematical induction. The positivity and the boundedness of solutions is proved using comprehensive mathematical techniques. Two main equilibrium points of the pandemic model are stated. The basic reproduction number for the model is computed using next generation technique to handle the future dynamics of the pandemic. We develop an optimal control problem to find the best controls for the quarantine and hospitalization strategies employed on exposed and infected humans, respectively. For numerical solution of the fractional model, we implemented the Adams–Bashforth method to prove the importance of order. A general fractional‐order optimal control problem and associated optimality conditions of Pontryagin type are discussed, with the goal to minimize the number of exposed and infected humans. The extremals are obtained numerically. [ FROM AUTHOR]
ABSTRACT
Messenger RNA has been studied by everyone, from vaccine developers to high school biology students, since the discovery of its isolation in 1961 [...].
ABSTRACT
This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized, and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo's sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17.
ABSTRACT
HIV-1 infection and its progression to AIDS remains a significant global health challenge, particularly for low-income countries. Developing a vaccine to prevent HIV-1 infections has proven to be immensely challenging with complex biological acquisition and infection, unforeseen clinical trial disappointments, and funding issues. This paper discusses important landmarks of progress in HIV-1 vaccine development, various vaccine strategies, and clinical trials.