Mathematical analysis and optimal control for Chikungunya virus with two routes of infection with nonlinear incidence rate

Abstract

Chikungunya fever, caused by Chikungunya virus (CHIKV) and transmitted to humans by infected Aedes mosquitoes, has posed a global threat in several countries. In this paper, we investigated a modified within-host Chikungunya virus (CHIKV) infection model with antibodies where two routes of infection are considered. In a first step, the basic reproduction number [Formula: see text] was calculated and the local and global stability analysis of the steady states is carried out using the local linearization and the Lyapunov method. It is proven that the CHIKV-free steady-state [Formula: see text] is globally asymptotically stable when [Formula: see text], and the infected steady-state [Formula: see text] is globally asymptotically stable when [Formula: see text]. In a second step, we applied an optimal strategy in order to optimize the infected compartment and to maximize the uninfected one. For this, we formulated a nonlinear optimal control problem. Existence of the optimal solution was discussed and characterized using some adjoint variables. Thus, an algorithm based on competitive Gauss–Seidel-like implicit difference method was applied in order to resolve the optimality system. The theoretical results are confirmed by some numerical simulations.

Periodic Trajectories for HIV Dynamics in a Seasonal Environment With a General Incidence Rate

“…It can be easily shown that W 0 = {E 0 }. Using LaSalle's invariance principle [26] (see [8,11,12,27] for some examples), one deduces that E 0 is globally asymptotically stable once R 0 ≤ 1.…”

“…Several works qualitatively proposed and studied some mathematical models describing the dynamical behaviour of infectious disease transmission (see, for example, [3][4][5][6][7][8][9]). In particular, the HIV epidemic models with constant coefficients have been analysed in several works (see, for example, [10][11][12][13]). However, seasonality is very repetitive in each of the ecological, biological, and human systems [14].…”

Multi-step semi-analytical solutions for a chikungunya virus system

“…Several mathematical models have been presented in the CHIKV infection literature to describe the evolution of disease transmission in a population over time or to describe the population growth of chikungunya virus within-host at each stage, see for example [1,3,18]. Modelling, mathematical analysis and optimal control for this virus have been studied by El Hajji et al in [19,20].…”

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 → +∞.…”

“…The main indicator in the spread of an epidemic is the force of infection or the rate at which a susceptible person becomes infected. The prediction models are mainly based on deterministic principles such as SIR or SEIR [6,7,8,9,10,11]. Recent SARS-CoV-2 models are often derived from the SIR model by adding a population of infected non-infectious E (or exposed) individuals who are therefore not contagious.…”