Dynamical analysis of monkeypox transmission incorporating optimal vaccination and treatment with cost-effectiveness.

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 ( R 0 h) and animals ( R 0 a) is obtained using the next-generation matrix technique. Depending on the values of R 0 h and R 0 a, 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 R 0 a = 1 for any value of R 0 h and at R 0 h = 1 for R 0 a < 1. 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 R 0 h and R 0 a are scaled.

Complex dynamics of a fractional-order SIR system in the context of COVID-19.

This paper proposes and analyses a new fractional-order SIR type epidemic model with a saturated treatment function. The detailed dynamics of the corresponding system, including the equilibrium points and their existence and uniqueness, uniform-boundedness, and stability of the solutions are studied. The threshold parameter, basic reproduction number of the system which determines the disease dynamics is derived, and the condition of occurrence of backward bifurcation is also determined. Some numerical works are conducted to validate our analytical results for the commensurate fractional-order system. Hopf bifurcations for the fractional-order system are studied by taking the order of the fractional differential as a bifurcation parameter.

The effectiveness of contact tracing in mitigating COVID-19 outbreak: A model-based analysis in the context of India.

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.

Modeling and control of COVID-19: A short-term forecasting in the context of India.

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.

A model based study on the dynamics of COVID-19: Prediction and control.

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.

Pulmonary Arterio-Venous Malformation (PAVM): A Rare Case Report.

A 6-year-old boy from Comilla, was admitted in Dhaka Medical College Hospital with exertional dyspnea, central cyanosis, clubbing and was finally diagnosed as pulmonary Arterio-Venous Malformation (PAVM) by bubble contrast echocardiography, and pulmonary CT angiography. As PAVM is rare in children, it is often not thought of in differential diagnoses and the diagnosis remains in disguise. In this report, we described the clinical presentation of 6-year-old child with PAVM and also how to investigate the case to get the diagnosis.

Complex Dynamics of an SIR Epidemic Model with Saturated Incidence Rate and Treatment.

This paper describes a traditional SIR type epidemic model with saturated infection rate and treatment function. The dynamics of the model is studied from the point of view of stability and bifurcation. Basic reproduction number is obtained and it is shown that the model system may possess a backward bifurcation. The global asymptotic stability of the endemic equilibrium is studied with the help of a geometric approach. Optimal control problem is formulated and solved. Some numerical simulation works are carried out to validate our analytical results.

A theoretical approach on controlling agricultural pest by biological controls.

In this paper we propose and analyze a prey-predator type dynamical system for pest control where prey population is treated as the pest. We consider two classes for the pest namely susceptible pest and infected pest and the predator population is the natural enemy of the pest. We also consider average delay for both the predation rate i.e. predation to the susceptible pest and infected pest. Considering a subsystem of original system in the absence of infection, we analyze the existence of all possible non-negative equilibria and their stability criteria for both the subsystem as well as the original system. We present the conditions for transcritical bifurcation and Hopf bifurcation in the disease free system. The theoretical evaluations are demonstrated through numerical simulations.

Sustainability and economic consequences of creating marine protected areas in multispecies multiactivity context.

The present study deals with harvesting of prey species in the presence of predator in a multispecies marine fishery. The total habitat is divided into two patches: one is reserve area where fishing is completely banned and other zone is called fishing area where only prey is exploited. We assume that the prey fish possesses heterogeneous intrinsic growth rate with uniform carrying capacity where as predator has constant intrinsic growth rate with prey dependent carrying capacity. The analytical conditions are derived to prevent the species extinction for larger employed effort in single (only prey) species fishery. Optimal equilibrium premium are presented for both monospecies and multispecies fishery for all degree of protection. Increasing standing stock (ISS) and protected standing stock (PSS) are measured in the presence of prey-predator interaction.

Possible ecosystem impacts of applying maximum sustainable yield policy in food chain models.

This paper describes the possible impacts of maximum sustainable yield (MSY) and maximum sustainable total yield (MSTY) policy in ecosystems. In general it is observed that exploitation at MSY (of single species) or MSTY (of multispecies) level may cause the extinction of several species. In particular, for traditional prey-predator system, fishing under combined harvesting effort at MSTY (if it exists) level may be a sustainable policy, but if MSTY does not exist then it is due to the extinction of the predator species only. In generalist prey-predator system, harvesting of any one of the species at MSY level is always a sustainable policy, but harvesting of both the species at MSTY level may or may not be a sustainable policy. In addition, we have also investigated the MSY and MSTY policy in a traditional tri-trophic and four trophic food chain models.

Maximum sustainable yield and species extinction in a prey-predator system: some new results.

Though the maximum sustainable yield (MSY) approach has been legally adopted for the management of world fisheries, it does not provide any guarantee against from species extinction in multispecies communities. In the present article, we describe the appropriateness of the MSY policy in a Holling-Tanner prey-predator system with different types of functional responses. It is observed that for both type I and type II functional responses, harvesting of either prey or predator species at the MSY level is a sustainable fishing policy. In the case of combined harvesting, both the species coexist at the maximum sustainable total yield (MSTY) level if the biotic potential of the prey species is greater than a threshold value. Further, increase of the biotic potential beyond the threshold value affects the persistence of the system.

An ecological perspective on marine reserves in prey-predator dynamics.

This paper describes a prey-predator type fishery model with prey dispersal in a two-patch environment, one of which is a free fishing zone and other is a protected zone. The existence of possible steady states, along with their local stability, is discussed. A geometric approach is used to derive the sufficient conditions for global stability of the system at the positive equilibrium. Relative size of the reserve is considered as control in order to study optimal sustainable yield policy. Subsequently, the optimal system is derived and then solved numerically using an iterative method with Runge-Kutta fourth-order scheme. Numerical simulations are carried out to illustrate the importance of marine reserve in fisheries management. It is noted that the marine protected area enables us to protect and restore multi-species ecosystem. The results illustrate that dynamics of the system is extremely interesting if simultaneous effects of a regulatory mechanism like marine reserve is coupled with harvesting effort. It is observed that the migration of the resource, from protected area to unprotected area and vice versa, is playing an important role towards the standing stock assessment in both the areas which ultimately control the harvesting efficiency and enhance the fishing stock up to some extent.

Dynamics of pest and its predator model with disease in the pest and optimal use of pesticide.

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.

Change in Normal Health Condition Due to COVID-19 Infection: Analysis by ANFIS Technique.

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.

An ANFIS model-based approach to investigate the effect of lockdown due to COVID-19 on public health.

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.

Modelling and control of a fractional-order epidemic model with fear effect.

In this paper, we formulate and study a new fractional-order SIS epidemic model with fear effect of an infectious disease and treatment control. The existence and uniqueness, nonnegativity and finiteness of the system solutions for the proposed model have been analysed. All equilibria of the model system are found, and their local and also global stability analyses are examined. Conditions for fractional backward and fractional Hopf bifurcation are also analysed. We study how the disease control parameter, level of fear and fractional order play a role in the stability of equilibria and Hopf bifurcation. Further, we have established our analytical results through several numerical simulations.

Harvesting induced stability and instability in a tri-trophic food chain.

Non-equilibrium dynamics in the form of oscillations or chaos is often found to be a natural phenomenon in complex ecological systems. In this paper, we first analyze a tri-trophic food chain, which is an extension of the Rosenzweig-MacArthur di-trophic food chain. We then explore the impact of harvesting individual trophic levels to answer the following questions : a) when a non-equilibrium dynamics persists, b) whether it can locally be stabilized to a steady state, c) when the system switches from a stable steady state to a non-equilibrium dynamics and d) whether the Maximum Sustainable Yield (MSY) always exists when the top predator is harvested. It is shown that searching for a general theory to unify the harvesting induced stability must take into account the number of trophic levels and the degree of species enrichment, the outcomes that cannot be obtained from the earlier reports on prey-predator models. We also identify the situation where harvesting induces instability switching: the non-equilibrium state enters into a stable steady-state and then, upon more intensive harvesting, the steady-state again loses its stability. One of the new and important results is also that the MSY may not exist for harvesting the top predator. In general, our results contribute to biological conservation theory, fishery and ecosystem biodiversity management.

Biological conservation through marine protected areas in the presence of alternative stable states.

This article addresses how depleted stock can be restored by creation of marine reserve and species mobility when alternative stable states persist in a marine ecosystem. To understand the role of a marine protected area, we develop a two-patch version of an originally single-patch model. In the two-patch model, we prove that some of the locally stable equilibria are not stable equilibria from an ecological viewpoint. Similarly, some unstable equilibria determined classically from the mathematical model are no longer equilibria. It is shown that increasing reserve size may produce three alternative stable states in the presence of harvesting. Dynamic solutions have a tendency to reach an upper stable state from a lower stable state when reserve size is increased, but the opposite phenomenon (i.e., shifting to a lower stable state from an upper one) never occurs. This suggests that MPAs always have a positive effect in stock conservation even when alternative stable states inherently persist in marine ecosystems.

Relationship between exploitation, oscillation, MSY and extinction.

We give answers to two important problems arising in current fisheries: (i) how maximum sustainable yield (MSY) policy is influenced by the initial population level, and (ii) how harvesting, oscillation and MSY are related to each other in prey-predator systems. To examine the impact of initial population on exploitation, we analyze a single species model with strong Allee effect. It is found that even when the MSY exists, the dynamic solution may not converge to the equilibrium stock if the initial population level is higher but near the critical threshold level. In a prey-predator system with Allee effect in the prey species, the initial population does not have such important impact neither on MSY nor on maximum sustainable total yield (MSTY). However, harvesting the top predator may cause extinction of all species if odd number of trophic levels exist in the ecosystem. With regard to the second problem, we study two prey-predator models and establish that increasing harvesting effort either on prey, predator or both prey and predator destroys previously existing oscillation. Moreover, equilibrium stock both at MSY and MSTY level is stable. We also discuss the validity of found results to other prey-predator systems.

A theoretical study on mathematical modelling of an infectious disease with application of optimal control.

In this paper, we propose and analyze an epidemic problem which can be controlled by vaccination as well as treatment. In the first part of our analysis we study the dynamical behavior of the system with fixed control for both vaccination and treatment. Basic reproduction number is obtained in all possible cases and it is observed that the simultaneous use of vaccination and treatment control is the most favorable case to prevent the disease from being epidemic. In the second part, we take the controls as time dependent and obtain the optimal control strategy to minimize both the infected populations and the associated costs. All the analytical results are verified by simulation works. Some important conclusions are given at the end of the paper.