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Seas, marine, and coastal regions are integral and essential parts of our ecosystem. Many scientific approaches have been taken to ensure the sustainable use of marine resources. Artificial intelligence (AI) plays a vital role in harvesting resources so that the system regenerates itself for the long term. This paper develops a two-input and two-output fuzzy logic-based model to predict the fisheries’ remaining biomass after harvesting and maintaining a high revenue level in the Bangladesh Sundarbans region. Fishing & tourism are taken as input parameters, and revenue & biomass are taken as output parameters. A total of 20 rules (IF-THEN type) have been generated in the fuzzy rule editor of Fuzzy Inference System (FIS), considering all possible combinations between input–output parameters. The data which we obtained from the real ecosystem exactly corresponds to the results that we got from our proposed model. Our fuzzy logic model yields valid predictions of the remaining biomass level without compromising profit, only by controlling the harvesting and tourist entry.

The COVID-19 pandemic has crippled the world population. Our present work aims to formulate a model to analyze the change in normal health conditions due to COVID-19 infection. For this purpose, we have collected data of seven parameters, namely, age, systolic pressure (SP), diastolic paper (DP), respiratory distress (RD), fasting blood sugar (FBS), cholesterol (CHL), and insomnia (INS) of 156 persons of Birnagar municipality, Nadia, India; before and after COVID-19 infection. Ultimately, using an adaptive neuro-fuzzy inference system (ANFIS), we have formulated our desired model, a Takagi-Sugeno fuzzy inference system. Further, with the help of this model, we have established one's change in health condition with age due to COVID-19 infection. Finally, we have derived that older people are more affected by COVID-19 infection than younger people.

In the present paper, we propose and study a fractional-order prey-predator type ecological model with the functional response of Holling type II and the effect of harvesting. In addition, we have also considered the influence of a super-predator on the conventional predator. The complex dynamical behaviour of the proposed model system including existence and uniqueness criteria, finiteness and nonnegativity of the solutions have studied rigorously. In addition, we have determined existence criteria of several equilibria and analyzed the asymptotic nature of those equilibria. We have enriched our analysis with the inclusion of fractional Hopf bifurcation and the criteria of global stability of the equilibrium points. Finally, some numerical simulation works have been incorporated to validate the analytical analysis.

The ongoing monkeypox outbreak that began in the UK has currently spread to every continent. Here, we use ordinary differential equations to build a nine-compartmental mathematical model to examine the dynamics of monkeypox transmission. The basic reproduction number for both humans ([Formula: see text]) and animals ([Formula: see text]) is obtained using the next-generation matrix technique. Depending on the values of [Formula: see text] and [Formula: see text], we discovered that there are three equilibria. The current study also looks at the stability of all equilibria. We discovered that the model experiences transcritical bifurcation at [Formula: see text] for any value of [Formula: see text] and at [Formula: see text] for [Formula: see text]. This is the first study that, to the best of our knowledge, has constructed and solved an optimal monkeypox control strategy while taking vaccination and treatment controls into consideration. The infected averted ratio and incremental cost-effectiveness ratio were calculated to evaluate the cost-effectiveness of all viable control methods. Using the sensitivity index technique, the parameters used in the formulation of [Formula: see text] and [Formula: see text] are scaled.

Presently, monkeypox virus infection has spread worldwide in the ongoing outbreak that began in the UK. To study the transmission dynamics of monkeypox, we formulate here a seven-compartmental (five compartments for the human population and two compartments for animals or rodents) fractional-order mathematical model. The existence and uniqueness of the solution of the proposed fractional order model are examined here. The basic reproduction number for humans ( R 0 h ) and animals ( R 0 a ) are obtained through the next-generation matrix approach. Depending on the values of R 0 h and R 0 a , we observed that the fractional order model has three equilibria, namely, monkeypox-free equilibrium, animal-free endemic equilibrium, and endemic equilibrium. Also, the stability of all equilibria is checked in this present article. We found that the model goes through transcritical bifurcation at R 0 a = 1 for any values of R 0 h and at R 0 h = 1 for R 0 a < 1 . Best of our knowledge, this is the first work where the fractional order optimal control for monkeypox is formulated and solved considering vaccination and treatment controls. Several feasible parameter values are used in the simulations to visualize and verify the findings, from which the results show that fractional order is more appropriate. Finally, parameters involved in the expression of R 0 h and R 0 a are scaled using the sensitivity index approach.

The infectious disease COVID-19 is a disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-COV-2) which has become a pandemic. RT-PCR test is implemented in most of the countries to diagnose the disease. Prioritizing individuals for RT-PCR test is necessary in this pandemic situation. In this scenario, we have attempted to propose and analyze two models on the vulnerability of COVID-19 for a person using fuzzy inference system (FIS) based on whether or not the person has a travelling history. To formulate these two models we have used Mamdani type Fuzzy Inference System. In these two models, ‘Hygiene’, ‘Immunity’, ‘Quarantine’ and ‘Home-isolation’ are taken as the inputs and ‘Vulnerability to COVID-19’ is taken as the output variable. A thorough study of these two models using FIS is done which suggests in what percentage a person is vulnerable to COVID-19.

COVID-19 has become one of the most severe health issues of the twenty-first century. More than 30 million people have been affected by this deadly disease and more than nine lakh people have been died due to this disease worldwide. Government authorities are forced to impose lockdown in their respective countries. In a word, COVID-19 has stopped the natural flow of life in worldwide. In this situation, scientists and researchers of different fields are trying to find out appropriate mitigating measures for COVID-19. However, there is no approved pharmaceutical measures like treatment or vaccination available to the health workers. So, the governments are strengthening on the non-pharmaceutical measures like maintaining social distance, use of face mask and sanitizer and on lockdown policy. In this scenario, determining the dynamics of the disease can help governments, health workers, scientists to decide future action to be taken in order to tackle the disease. In this chapter, we have proposed and analyzed an SEAIR type fractional order epidemic model in order to investigate the transmission mechanisms of the COVID-19. We have studied the non-negativity and boundedness of the solutions, and the existence and uniqueness of the solutions of the system. The explicit expression of the most important parameter, namely the basic reproduction number is derived and the further investigations of the system are performed in terms of the basic reproduction number. Apart from studying the local dynamics of the fractional order system, we have considered the environmental fluctuations in the deterministic system. We have studied the stochastic stability of the infected equilibrium points. Finally, important results are illustrated through numerical simulation works.

During the first and second quarters of the year 2020, most of the countries had implemented complete or partial lockdown policies to slow down the transmission of the COVID-19. To cultivate the effect of lockdown due to COVID-19 on public health, we have collected the data of six primary parameters, namely systolic blood pressure, diastolic blood pressure, fasting blood sugar, insomnia, cholesterol, and respiratory distress of 200 randomly chosen people from a municipality region of West Bengal, India before and after lockdown. With the help of these data and Adaptive Neuro-Fuzzy Inference System (ANFIS), we have formulated a model that has established that lockdown due to COVID-19 has negligible impacts on the individuals with better health condition but has significant effects on the health conditions to those populations who have poor health.

In this paper, a three species food chain model has been developed among the interaction of prey, predator and super predator. It is assumed that the predator shows refuge behavior to the super predator. It is also assumed that a certain amount of additional food will be supplied to the super predator. It is considered that the predator population is benefiting partially from the additional food. To get optimal harvesting of super predator the Pontryagin’s maximum principle has been used. It is found that super predator may be extinct if harvesting rate increase. It is observed that as the refuge rate increases, predator population gradually increases, but super predator population decreases. Also, it is found that our proposed system undergoes oscillatory or periodic behavior as the value of refuge rate (m1), harvesting rate (E), the intrinsic growth rate of prey (r), carrying capacity of prey (k) and conservation rate of prey (c1) varies for some certain range of these parameters. It is found that this study may be useful for the increase of harvesting of a super predator by supplying the additional food to our proposed system.

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.

The coronavirus disease 2019 (COVID-19) outbreak, due to SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), originated in Wuhan, China and is now a global pandemic. The unavailability of vaccines, delays in diagnosis of the disease, and lack of proper treatment resources are the leading causes of the rapid spread of COVID-19. The world is now facing a rapid loss of human lives and socioeconomic status. As a mathematical model can provide some real pictures of the disease spread, enabling better prevention measures. In this study, we propose and analyze a mathematical model to describe the COVID-19 pandemic. We have derived the threshold parameter basic reproduction number, and a detailed sensitivity analysis of this most crucial threshold parameter has been performed to determine the most sensitive indices. Finally, the model is applied to describe COVID-19 scenarios in India, the second-largest populated country in the world, and some of its vulnerable states. We also have short-term forecasting of COVID-19, and we have observed that controlling only one model parameter can significantly reduce the disease's vulnerability.

The ongoing pandemic situation due to COVID-19 originated from the Wuhan city, China affects the world in an unprecedented scale. Unavailability of totally effective vaccination and proper treatment regimen forces to employ a non-pharmaceutical way of disease mitigation. The world is in desperate demand of useful control intervention to combat the deadly virus. This manuscript introduces a new mathematical model that addresses two different diagnosis efforts and isolation of confirmed cases. The basic reproductive number, R 0 , is inspected, and the model’s dynamical characteristics are also studied. We found that with the condition R 0 1 , the disease can be eliminated from the system. Further, we fit our proposed model system with cumulative confirmed cases of six Indian states, namely, Maharashtra, Tamil Nadu, Andhra Pradesh, Karnataka, Delhi and West Bengal. Sensitivity analysis carried out to scale the impact of different parameters in determining the size of the epidemic threshold of R 0 . It reveals that unidentified symptomatic cases result in an underestimation of R 0 whereas, diagnosis based on new contact made by confirmed cases can gradually reduce the size of R 0 and hence helps to mitigate the ongoing disease. An optimal control problem is framed using a control variable u ( t ) , projecting the effectiveness of diagnosis based on traced contacts made by a confirmed COVID patient. It is noticed that optimal contact tracing effort reduces R 0 effectively over time.

This paper describes a prey–predator type ecological model with infection in the prey populations. We also consider here a nonlinear functional response for disease transmission and a constant amount of refuge for the sound prey populations. The dynamical behavior of the mathematical model is described from the point of view of stability and bifurcation. A geometric method is also applied to establish the global asymptotic stability at the co-existence equilibrium point. Some computer simulation works have been presented to illustrate the theoretical results.

In this paper, we proposed and analyzed a susceptible-infected-recovered (SIR) type epidemic model to investigate the effect of transport-related infectious diseases namely tuberculosis, measles, rubella, influenza, sexually transmitted diseases, etc. The existence and stability criteria of both the diseases include free equilibrium point and endemic equilibrium point which are established and the threshold parametric condition for which the system passes through a transcritical bifurcation is also obtained. Optimal control strategy for control parameters is formulated and solved both theoretically and numerically. Lastly, we not only illustrate our theoretical results through graphical illustrations but also computer simulation is used to show that our model would be a good model to study the SARS epidemic in 2003.

In this paper we have proposed and analyzed a simple three-dimensional mathematical model related to malaria disease. We consider three state variables associated with susceptible human population, infected human population and infected mosquitoes, respectively. A discrete delay parameter has been incorporated to take account of the time of incubation period with infected mosquitoes. We consider the effect of insecticide control, which is applied to the mosquitoes. Basic reproduction number is figured out for the proposed model and it is shown that when this threshold is less than unity then the system moves to the disease-free state whereas for higher values other than unity, the system would tend to an endemic state. On the other hand if we consider the system with delay, then there may exist some cases where the endemic equilibrium would be unstable although the numerical value of basic reproduction number may be greater than one. We formulate and solve the optimal control problem by considering insecticide as the control variable. Optimal control problem assures to obtain better result than the noncontrol situation. Numerical illustrations are provided in support of the theoretical results.

Spatial heterogeneity is an important aspect to be studied in infectious disease models. It takes two forms: one is local, namely diffusion in space, and other is related to travel. With the advancement of transportation system, it is possible for diseases to move from one place to an entirely separate place very quickly. In a developing country like India, the mass movement of large numbers of individuals creates the possibility of spread of common infectious diseases. This has led to the study of infectious disease model to describe the infection during transport. An SIRS-type epidemic model is formulated to illustrate the dynamics of such infectious disease propagation between two cities due to population dispersal. The most important threshold parameter, namely the basic reproduction number, is derived, and the possibility of existence of backward bifurcation is examined, as the existence of backward bifurcation is very unsettling for disease control and it is vital to know from modeling analysis when it can occur. It is shown that dispersal of populations would make the disease control difficult in comparison with nondispersal case. Optimal vaccination and treatment controls are determined. Further to find the best cost-effective strategy, cost-effectiveness analysis is also performed. Though it is not a case study, simulation work suggests that the proposed model can also be used in studying the SARS epidemic in Hong Kong, 2003.

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.

In this paper, a predator-prey interaction model among juvenile prey, adult prey and predator has been developed where stage structure is considered on prey species. The functional responses has been considered as ratio dependent. It is assumed that that the adult prey is strong enough such that it has an anti-predator characteristic. Global dynamics of the co-existing equilibrium point has been discussed with the help of the geometric approach. Furthermore, it is established that the proposed system undergoes through a Hopf bifurcation with respect to some important parameters. Finally, some numerical simulations have been done to test our theoretical results.

In this paper, we propose and analyze a fractional-order SIS epidemic model with the saturated treatment and disease transmission. The existence and uniqueness, nonnegativity and finiteness of solutions for our suggested model have been studied. Different equilibria of the model are found and their local and global stability analyses are also examined. Furthermore, the conditions for fractional backward and fractional Hopf bifurcation are also analyzed in both the commensurate and incommensurate fractional-order model. We study how the control parameter and the order of the fractional derivative play role in local as well as global stability of equilibrium points and Hopf bifurcation. We have demonstrated the analytical results of our proposed model system through several numerical simulations.

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.