In this paper, we proposed a nonlinear deterministic mathematical model for the transmission dynamics of COVID-19. First, we analyzed the system properties such as boundedness of the solutions, existence of disease-free and endemic equilibria, local and global stability of equilibrium points. Besides, we computed the basic reproduction number and studied its normalized sensitivity for model parameters to identify the most influencing parameter. The local stability of the disease-free equilibrium point is also verified via the help of the Jacobian matrix and Routh Hurwitz criteria. Moreover, the global stability of the disease-free equilibrium point is proved by using the approach of Castillo-Chavez and Song. We also proved the existence of the forward bifurcation using the center manifold theory. Then the model is fitted with COVID-19 infected cases reported from March 13, 2020, to July 31, 2021, in Ethiopia. The values of model parameters are then estimated from the data reported using the least square method together with the fminsearch function in the MATLAB optimization toolbox. Finally, different simulation cases were performed using PYTHON software to compare with analytical results. The simulation results suggest that the spread of COVID-19 can be managed via minimizing the contact rate of infected and increasing the quarantine of exposed individuals.

In this paper, we apply optimal control theory to a novel coronavirus transmission model given by a system of non-linear ordinary differential equations. Optimal control strategies are obtained by minimizing the number of exposed and infected population considering the cost of implementation. The existence of optimal controls and characterization is established using Pontryagin's Maximum Principle. An expression for the basic reproduction number is derived in terms of control variables. Then the sensitivity of basic reproduction number with respect to model parameters is also analysed. Numerical simulation results demonstrated good agreement with our analytical results. Finally, the findings of this study shows that comprehensive impacts of prevention, intensive medical care and surface disinfection strategies outperform in reducing the disease epidemic with optimum implementation cost.

Tuberculosis (TB) and coronavirus (COVID-19) are both infectious diseases that globally continue affecting millions of people every year. They have similar symptoms such as cough, fever, and difficulty breathing but differ in incubation periods. This paper introduces a mathematical model for the transmission dynamics of TB and COVID-19 coinfection using a system of nonlinear ordinary differential equations. The well-posedness of the proposed coinfection model is then analytically studied by showing properties such as the existence, boundedness, and positivity of the solutions. The stability analysis of the equilibrium points of submodels is also discussed separately after computing the basic reproduction numbers. In each case, the disease-free equilibrium points of the submodels are proved to be both locally and globally stable if the reproduction numbers are less than unity. Besides, the coinfection disease-free equilibrium point is proved to be conditionally stable. The sensitivity and bifurcation analysis are also studied. Different simulation cases were performed to supplement the analytical results.

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International audienceThe aim of this article is to propose an optimization strategy for traffic flow on roundabouts using a macroscopic approach. The roundabout is modeled as a sequence of 2 × 2 junctions with one main-lane and secondary incoming and outgoing roads. We consider two cost functionals: the total travel time and the total waiting time, which give an estimate of the time spent by drivers on the network section. These cost functionals are minimized with respect to the right of way parameter of the incoming roads. For each cost functional, the analytical expression is given for each junction. We then solve numerically the optimization problem and show some numerical results

In this study, we proposed and analyzed the optimal control and cost-effectiveness strategies for malaria epidemics model with impact of temperature variability. Temperature variability strongly determines the transmission of malaria. Firstly, we proved that all solutions of the model are positive and bounded within a certain set with initial conditions. Using the next-generation matrix method, the basic reproductive number at the present malaria-free equilibrium point was computed. The local stability and global stability of the malaria-free equilibrium were depicted applying the Jacobian matrix and Lyapunov function respectively when the basic reproductive number is smaller than one. However, the positive endemic equilibrium occurs when the basic reproductive number is greater than unity. A sensitivity analysis of the parameters was conducted; the model showed forward and backward bifurcation. Secondly, using Pontryagin’s maximum principle, optimal control interventions for malaria disease reduction are described involving three control measures, namely use of insecticide-treated bed nets, treatment of infected humans using anti-malarial drugs, and indoor residual insecticide spraying. An analysis of cost-effectiveness was also conducted. Finally, based on the simulation of different control strategies, the combination of treatment of infected humans and insecticide spraying was proved to be the most efficient and least costly strategy to eradicate the disease.

In this paper, we proposed and analyzed a nonlinear deterministic model for the impact of temperature variability on the epidemics of the malaria. The model analysis showed that all solutions of the systems are positive and bounded with initial conditions in a certain set. Thus, the model is proved to be both epidemiologically meaningful and mathematically well-posed. Using the next-generation matrix approach, the basic reproduction number with respect to the disease-free equilibrium (DFE) point is obtained. The local stability of the equilibria points is shown using the Routh–Hurwitz criterion. The global stability of the equilibria points is performed using the Lyapunov function. Also, we proved that if the basic reproduction number is less than one, the DFE is locally and globally asymptotically stable. But, if the basic reproduction number is greater than one, the unique endemic equilibrium exists, locally and globally asymptotically stable. The sensitivity analysis of the parameters is also described. Moreover, we used the method implemented by the center manifold theorem to identify that the model exhibits forward and backward bifurcations. From our analytical results, we confirmed that the variation of temperature plays a significant role on the transmission of malaria. Lastly, numerical simulations are demonstrated to enhance the analytical results of the model.