Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate

Abstract

In this article, we examine the dynamics of a Chikungunya virus (CHIKV) infection model with two routes of infection. The model uses four categories, namely, uninfected cells, infected cells, the CHIKV virus, and antibodies. The equilibrium points of the model, which consist of the free point for the CHIKV and CHIKV endemic point, are first analytically determined. Next, the local stability of the equilibrium points is studied, based on the basic reproduction number (R0) obtained by the next-generation matrix. From the analysis, it is found that the disease-free point is locally asymptotically stable if R0≤1, and the CHIKV endemic point is locally asymptotically stable if R0>1. Using the Lyapunov method, the global stability analysis of the steady-states confirms the local stability results. We then describe our design of an optimal recruitment strategy to minimize the number of infected cells, as well as a nonlinear optimal control problem. Some numerical simulations are provided to visualize the analytical results obtained.

Mathematical Analysis for the Influence of Seasonality on Chikungunya Virus Dynamics

“…In this paper, we extended the CHIKV epidemic mathematical models studied in [1][2][3]19] by considering the impact of seasonality. We defined the basic reproduction number, R 0 trough a linear integral operator.…”

“…Finally, if the problem is well posed, the next step then consists of solving this problem, that is to say, analyzing the model in order to understand, to predict and act. Several models have been proposed to describe the transmission dynamics of vector-borne diseases [1][2][3][4][5][6][7][8]. Since several infectious diseases exhibit seasonal peak periods, then studying the impact of seasonal environment becomes a necessity to more understand such a disease transmission [9][10][11][12][13][14][15][16].…”

Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics

“…It can be easily shown that W1 = { Ē} . Using LaSalle's invariance principle [14] (see [15,16,17,9,10,11,18,19] for more applications), one can easily deduce that Ē is GAS when R ≤ 1. Then the solution of system (2.1) converges to Ē since t → +∞.…”

Mathematical Modeling for a CHIKV Transmission Under the Influence of Periodic Environment

“…Several researchers worked on some mathematical models for several infectious diseases [1][2][3][4][5][6][7]. In particular, the modeling of the behavior of CHIKV dynamics was studied in several recent works [8][9][10][11][12][13][14][15].…”