Gradient-based Instantaneous Traffic Flow Optimization on a Roundabout

In this article we focus on instantaneous traffic fl ow optimization on a roundabout using a macroscopic approach. The roundabout is modeled as a concatenation of 2x2 junctions with one main lane and secondary incoming and outgoing roads. We consider a cost functional that measures the total travel time spent by drivers on the roundabout and compute its gradient with respect to the priority parameters at junctions. Then, through numerical simulations, the traffic behavior is studied on the whole roundabout. The numerical approximations compare the performance of a roundabout for instantaneous optimization of the priority parameters and fixed constant parameters

Optimal Control and Cost Effectiveness Analysis of SIRS Malaria Disease Model with Temperature Variability Factor

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

Gradient-based Instantaneous Traffic Flow Optimization on a Roundabout

In this article we focus on instantaneous traffic fl ow optimization on a roundabout using a macroscopic approach. The roundabout is modeled as a concatenation of 2x2 junctions with one main lane and secondary incoming and outgoing roads. We consider a cost functional that measures the total travel time spent by drivers on the roundabout and compute its gradient with respect to the priority parameters at junctions. Then, through numerical simulations, the traffic behavior is studied on the whole roundabout. The numerical approximations compare the performance of a roundabout for instantaneous optimization of the priority parameters and fixed constant parameters

Farming awareness based optimum interventions for crop pest control

We develop a mathematical model, based on a system of ordinary differential equations, to the upshot of farming alertness in crop pest administration, bearing in mind plant biomass, pest, and level of control. Main qualitative analysis of the proposed mathematical model, akin to both pest-free and coexistence equilibrium points and stability analysis, is investigated. We show that all solutions of the model are positive and bounded with initial conditions in a certain significant set. The local stability of pest-free and coexistence equilibria is shown using the Routh-Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pest-free equilibrium is locally asymptotically stable. To get optimum interventions for crop pests, that is, to decrease the number of pests in the crop field, we apply optimal control theory and find the corresponding optimal controls. We establish existence of optimal controls and characterize them using Pontryagin's minimum principle. Finally, we make use of numerical simulations to illustrate the theoretical analysis of the proposed model, with and without control measures.Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Mathematical Biosciences and Engineering', available in [https://doi.org/10.3934/mbe.2021272]. Please cite this article as: T. Abraha, F. Al Basir, L. L. Obsu and D. F. M. Torres, Farming awareness based optimum interventions for crop pest control, Math. Biosci. Eng. 18 (2021), no. 5, 5364--539

Macroscopic traffic flow optimization on roundabouts

The aim of this paper 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 with one mainline and secondary incoming and outgoing roads. We consider two cost the total travel time and the total waiting time, which give an estimate of the time by drivers on the network section. These cost functionals are minimized with respect to the of way parameter of the incoming roads. For each cost functional, the analytical expression given for each junction

Analysis of Traffic Evolution on Road Networks of a Roundabout

In this paper, the analyses of traffic evolution on the road network of a roundabout having three entrances and three exiting legs are conducted from macroscopic point of view. The road networks of roundabouts are modeled as a merging and diverging types 1×2 and 2×1 junctions. To study traffic evolution at junction, two cases have been considered, namely, demand and supply limited cases. In each case, detailed mathematical analysis and numerical tests have been presented. The analysis in the case of demand limited showed that rarefaction wave fills the portion of the road network in time. In the contrary, in supply limited case, traffic congestion occurs at merging junctions and shock wave propagating back results in reducing the performance of a roundabout to control traffic dynamics. Also, we illustrate density and flux profiles versus space discretization at different time steps via numerical simulation with the help of Godunov scheme

Pest control using farming awareness: impact of time delays and optimal use of biopesticides

We investigate a mathematical model in crop pest management, considering plant biomass, pest, and the effect of farming awareness. The pest population is divided into two compartments: susceptible pest and infected pest. We assume that the growth rate of self-aware people is proportional to the density of healthy pests present in the crop field. Impacts of awareness is modeled via a saturated term. It is further assumed that self-aware people will adopt biological control methods, namely integrated pest management. Susceptible pests are detrimental to crops and, moreover, there may be some time delay in measuring the healthy pests in the crop field. A time delay may also take place while becoming aware of the control strategies or taking necessary steps to control the pest attack. In agreement, we develop our model incorporating two time delays into the system. The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays. Stability switches occur through Hopf-bifurcation when time delays cross critical values. Optimal control theory has been applied for the cost-effectiveness of the delayed system. Numerical simulations illustrate the obtained analytical results.publishe

Controlling crop pest with a farming awareness based integrated approach and optimal control

We investigate a mathematical model in crop pest controlling, considering plant biomass, pest, and the effect of farming awareness. The pest population is divided into two compartments: susceptible pests and infected pests. We assume that the growth rate of self-aware people is proportional to the density of susceptible pests existing in the crop arena. Impacts of awareness are modeled through the usual mass action term and a saturated term. It is further assumed that self-aware people will adopt chemical and biological control methods, namely integrated pest management. Bio-pesticides are costly and require a long-term process, expensive to impose. However, if chemical pesticides are introduced in the farming system along with bio-pesticides, the process will be faster as well as cost-effective. Also, farming knowledge is equally important. In this article, a mathematical model is derived for controlling crop pests through an awareness-based integrated approach. In order to reduce the negative effects of pesticides, we apply optimal control theory.Adama Science and Technology University (ASTU), ASTU/SP-R/027/19; Fundação para a Ciência e a Tecnologia, UIDB/04106/2020 (CIDMA).publishe

Optimal Control Strategy on Mathematical Model for the Dynamics of Mastitis

Inthisstudy,anonlinearmathematicalmodelforthetransmissiondynamicsofmastitisdiseasesisformulatedandanalyzed. The local and global stability analysis of mastitis-free equilibrium and endemic equilibrium is obtained using the stability theory of differential equation. It was established that the mastitis-free equilibrium is locally stable if the basic reproduction number is less than unity. The endemic equilibrium, which exists only when the basic reproduction number is greater than unity, is globally asymptotically stable. Sensitivity analysis of the reproduction number suggested that the concentration of bacteria in the environment has a high impact on the dynamics of mastitis. Furthermore, an optimal control problem is formulated by applying Pontryagin’s minimum principle with three control strategies, namely, prevention strategy, screening strategy, and treatment strategy. Therefore, based on optimal control problem simulation results and analysis of cost-effectiveness prevention strategy is the most effective and least costly to eradicate the transmission of mastitis from the cattle