Tuberculosis and COVID-19 are among the diseases with major global public health concern and great socio-economic impact. Co-infection of these two diseases is inevitable due to their geographical overlap, a potential double blow as their clinical similarities could hamper strategies to mitigate their spread and transmission dynamics. To theoretically investigate the impact of control measures on their long-term dynamics, we formulate and analyze a mathematical model for the co-infection of COVID-19 and tuberculosis. Basic properties of the tuberculosis only and COVID-19 only sub-models are investigated as well as bifurcation analysis (possibility of the co-existence of the disease-free and endemic equilibria). The disease-free and endemic equilibria are globally asymptotically stable. The model is extended into an optimal control system by incorporating five control measures. These are: tuberculosis awareness campaign, prevention against COVID-19 (e.g., face mask, physical distancing), control against co-infection, tuberculosis and COVID-19 treatment. Five strategies which are combinations of the control measures are investigated. Strategy B which focuses on COVID-19 prevention, treatment and control of co-infection yields a better outcome in terms of the number of COVID-19 cases prevented at a lower percentage of the total cost of this strategy.

We consider an unconditional fully discrete finite element scheme for a nematic liquid crystal flow with different kinematic transport properties. We prove that the scheme converges towards a unique critical point of the elastic energy subject to the finite element subspace, when the number of time steps go to infinity while the time step and mesh size are fixed. A Lojasiewicz type inequality, which is the key for getting the time asymptotic convergence of the whole sequence furnished by the numerical scheme, is also derived.

This paper studies fishery strategies in lakes, seas, and shallow rivers subject to agricultural and industrial pollution. The flowing pollutants are modeled by a nonlinear differential equation in a general manner. The logistic growth model for the fish population is modified to cover the pollution impact on the fish growth rate. We start by presenting the stability analysis of the dynamical system to discern the different types of the evolution of the fish population according to human actions. A cooperative game is formulated to design strategies for preserving the fish population by controlling the pollution as well as the fish stock for harvesting. The sufficient conditions for implementing the cooperative strategy are investigated through an incentive design approach with an adaptive taxation policy for the players. Numerical results are presented to illustrate the benefit of the cooperative for fish population preservation but also for the players’ rewards.

This paper treats a water flow regularization problem by means of local boundary conditions for the two-dimensional viscous shallow water equations. Using an a-priori energy estimate of the perturbation state and the Faedo–Galerkin method, we build a stabilizing boundary feedback control law for the volumetric flow in a finite time that is prescribed by the solvability of the associated Cauchy problem. We iterate the same approach to build by cascade a stabilizing feedback control law for infinite time. Thanks to a positive arbitrary time-dependent stabilization function, the control law provides an exponential decay of the energy.