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In the present study, we develop and analyze an SEIR epidemic model to assess the consequences of media awareness program and treatment control. The disease transmission rate as well as the treatment function are taken in the saturated form. Different equilibrium points and their stability are discussed. The threshold parameter, basic reproduction number is obtained and it is seen that the system may posses a backward bifurcation. An optimal control problem is formulated with treatment and media awareness parameters as control parameters and solved it analytically. The cost-effectiveness analysis is performed to find out the best strategy to be applied to control the transmission of diseases. In addition to our analytical results, several numerical simulations are also illustrated. Finally, a brief discussion is given regarding the role of treatment and media awareness program.

Japanese encephalitis (JE) is a public health problem that threats the entire world today. Japanese Encephalitis virus (JEV) mostly became a threat due to the significant number of increase of susceptible mosquito vectors and vertebrate hosts in Asia by which around 70,000 cases and 10,000 deaths per year took place in children below 15 years of age. In this paper, a mathematical model of JE due to JEV from the vector source (infected mosquito) and two vertebrate hosts (infected human and infected pig) is formulated. The disease can be controlled by applying several control measures such as vaccination, medicine and insecticide to the JE infection causing species. The model has been formulated as an optimal control problem and has been solved using Pontryagin's maximum principle. Also, the stability of the system has been studied with the help of basic reproduction number for disease free and endemic equilibrium. The results of fixed control for endemic equilibrium is presented numerically and depicted graphically. The effects of different control strategies on human, pig and mosquito has been analyzed using Runge-Kutta 4th order forward and backward techniques and presented thereafter graphically.

Recently the vector-borne disease dengue has become one of those infectious diseases with the potential of becoming endemic. Though dengue fever may occur at any time of the year, it depends very much on a suitable environment. Taking this into account, in this work we have developed a mathematical model using type-2 fuzzy inference system to predict suitable conditions for dengue outbreak so that control measures can be implemented as soon as possible. Here temperature, rainfall, humidity is taken as input parameters and the chance of dengue fever is taken as the output parameter. To understand the system easily we have used MATLAB software to generate various simulation works.

Highlights • A mathematical model has been proposed to analyse the pandemic COVID-19. • The model has been analysed both theoretically and numerically. • The procedure to control the basic reproduction number R 0 has been provided. • We have formed an optimal control problem where governmental policy is the control. • The model is used for short term prediction of COVID-19 in three states of India., As there is no vaccination and proper medicine for treatment, the recent pandemic caused by COVID-19 has drawn attention to the strategies of quarantine and other governmental measures, like lockdown, media coverage on social isolation, and improvement of public hygiene, etc to control the disease. The mathematical model can help when these intervention measures are the best strategies for disease control as well as how they might affect the disease dynamics. Motivated by this, in this article, we have formulated a mathematical model introducing a quarantine class and governmental intervention measures to mitigate disease transmission. We study a thorough dynamical behavior of the model in terms of the basic reproduction number. Further, we perform the sensitivity analysis of the essential reproduction number and found that reducing the contact of exposed and susceptible humans is the most critical factor in achieving disease control. To lessen the infected individuals as well as to minimize the cost of implementing government control measures, we formulate an optimal control problem, and optimal control is determined. Finally, we forecast a short-term trend of COVID-19 for the three highly affected states, Maharashtra, Delhi, and Tamil Nadu, in India, and it suggests that the first two states need further monitoring of control measures to reduce the contact of exposed and susceptible humans.

In South Asian countries, Tenualosa ilisha, well known as Hilsa, is considered as one of the most economically important fish species. Production of Hilsa fishes depends on many factors including global warming, water pollution and harvesting. This article proposes a new mathematical model using fuzzy inferences to investigate the impacts of global warming, water pollution and harvesting of juvenile fishes on the production of mature Hilsa fishes. Mamdani inference method has been applied for the fuzzy rule-based model. The model is executed by using the Fuzzy Logic Toolbox of MATLAB.

In the present paper we consider an SEIR type epidemic model with transport related infection between two cities. It is observed that transportation among regions has a strong impact on the dynamic evolution of a disease which can be eradicated in the absence of transportation. Transportation can lead to the incorporation of a positive risk probability. The epidemiological threshold, commonly known as the basic reproduction number, is derived and it is observed that when the basic reproduction number is less than unity the disease dies out, where as if it exceeds unity the disease may persist in the system. A thorough dynamical behavior of the constructed model is studied. We formulate and solve an optimal control problem using vaccination as a control tool. Extensive numerical simulations are carried out based on our analytical results. Finally we try to relate our work with a real world problem.

In this paper, we propose and analyze a prey–predator system consisting of two competitive prey populations and one predator population which depends on both the prey species. We investigate the boundedness and persistence criteria of the system and existence conditions of all the possible equilibria. Further the dynamical behavior from the point of view of local and global stability at different equilibria are presented. We also determine the explicit conditions so that the system has no periodic solutions. Finally, we present some numerical examples to illustrate our analytical works.

We have proposed and analyzed a vector-borne disease model with three types of controls for the eradication of the disease. Four different classes for the human population namely susceptible, infected, recovered and vaccinated and two different classes for the vector populations namely susceptible and infected are considered. In the first part of our analysis the disease dynamics are described for fixed controls and some inferences have been drawn regarding the spread of the disease. Next the optimal control problem is formulated and solved considering control parameters as time dependent. Different possible combination of controls are used and their effectiveness are compared by numerical simulation.

A three dimensional ecoepidemiological model consisting of susceptible prey, infected prey and predator is proposed and analysed in the present work. The parameter delay is introduced in the model system for considering the time taken by a susceptible prey to become infected. Mathematically we analyze the dynamics of the system such as, boundedness of the solutions, existence of non-negative equilibria, local and global stability of interior equilibrium point. Next we choose delay as a bifurcation parameter to examine the existence of the Hopf bifurcation of the system around its interior equilibrium. Moreover we use the normal form method and center manifold theorem to investigate the direction of the Hopf bifurcation and stability of the bifurcating limit cycle. Some numerical simulations are carried out to support the analytical results.

This paper describes a prey-predator model with Holling type II functional response incorporating prey refuge. The equilibria of the proposed system are determined and the behavior of the system is investigated around equilibria. Density-dependent mortality rate for the predator is considered as bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the co-existing equilibrium point. Discrete-type gestational delay of predators is also incorporated on the system. The dynamics of the delay induced prey-predator system is analyzed. Delay preserving stability and direction of the system is studied. Global stability of the delay preserving system is shown. Finally, some numerical simulations are given to verify the analytical results, and the system is analyzed through graphical illustrations.

In this paper, we propose and analyze a prey-predator system. Here the prey population is taken as pest and the predators are those eat the pests. Moreover we assume that the prey species is infected with a viral disease forming into susceptible and infected classes and infected prey is more vulnerable to predation by the predator. The dynamical behavior of this system both analytically and numerically is investigated from the point of view of stability and bifurcation. Then we explicitly introduce a control variable for pest control into the analysis by considering the associated control cost. In the nonconstant control case, we use Pontrygin's Maximum principle to derive necessary conditions for the optimal control of the pest. Then we demonstrated the analytical results by numerical analysis and characterized the effects of the parameter values on optimal strategy.

This paper describes a prey–predator model with stage structure for predator and selective harvesting effort on predator population. The Holling type II functional response function is taken into consideration. All the equilibria of the proposed system are determined and the behavior of the system is investigated near them. Local stability of the system is analyzed. Geometric approach is used to derive the sufficient conditions for global stability of the system. The occurrence of Hopf bifurcation of the model system in the neighborhood of the co-existing equilibrium point is shown through considering maximal relative increase of predation as bifurcation parameter. Fishing effort used to harvest predator population is considered as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent earned from the resource. Pontryagin’s maximum principle is used to characterize the optimal control. The optimal system is derived and then solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem.