Dynamics of a stage-structured predator-prey system with fear-induced group defense in autonomous and nonautonomous settings.

In this investigation, we construct a predator-prey model that distinguishes between immature and mature prey, highlighting group defense strategies within the mature prey. First, we embark on exploring the positivity and boundedness of the solution, unraveling sustainable equilibrium points, and deducing their stability conditions. Upon further investigation, we observe that the system exhibits diverse bifurcations, including Hopf, saddle-node, transcritical, generalized Hopf, cusp, and Bogdanov-Takens bifurcations. The results reveal that heightened fear decreases mature prey density, potentially causing prey extinction beyond a certain threshold. Increased maturation rates lead to the coexistence of immature and mature prey populations and higher predator density. Stronger group defense boosts mature prey density, while weaker defense results in weak persistence. Lower values of the maturation rate of prey and the decline rate of predators sustain only the predator population, reliant on resources other than focal prey. Furthermore, our model demonstrates intriguing and diverse dynamical phenomena, including various forms of bistability across distinct bi-parameter planes. We also explore the dynamics of a related nonautonomous system, where certain parameters are considered to vary with time. In the seasonally forced model, we set out to define criteria regarding the existence and stability of positive periodic solutions. Numerical investigations into the seasonally forced model uncover a spectrum of dynamics, ranging from simple periodic solutions to higher periodicities, bursting patterns, and chaotic behavior.

Impact of saturated treatments on HIV-TB dual epidemic as a consequence of COVID-19: optimal control with awareness and treatment.

In this study, we propose an HIV-TB co-infection model by considering the treatment provision limitation induced by recent COVID-19 pandemic that impacts this dual epidemic immensely, assimilating the significance of educational attempts. We analyze the model and its submodels with single infections individually. We obtain the awareness-induced basic reproduction numbers and discuss the global stability of disease-free equilibrium when provision limitation is zero. We observe that the submodels exhibit forward as well as backward bifurcations under provision restriction. Further, we derive thresholds for resource limitations regulating the dynamical behavior of the systems while analyzing the stability of endemic equilibrium of the models with single infections. Sophisticated simulation approaches are implemented to discover the influences of provision-restricted medication and awareness on dual epidemic. Our findings convey the persistence of co-infection though the basic reproduction number is below unity, if the provision restriction remains uncurbed. An observable insight is that, in spite of having epidemic threshold less than unity and no limitation in TB treatment, co-infection relapses and persists in the population, when there is no awareness attempt. Numerical findings emphasize the urgent need of increased treatment accessibility and importance of awareness in the current situation. Moreover, an optimization problem incorporating treatment and awareness controls is formulated and solved to find the ideal strategy to manage HIV-TB co-epidemic that recommends to diminish the medical resource limitation to get the enormous impact in dominating the adversity caused by COVID-19.

Impact of social media advertisements on the transmission dynamics of COVID-19 pandemic in India.

In this paper, we propose a mathematical model to assess the impact of social media advertisements in combating the coronavirus pandemic in India. We assume that dissemination of awareness among susceptible individuals modifies public attitudes and behaviours towards this contagious disease which results in reducing the chance of contact with the coronavirus and hence decreasing the disease transmission. Moreover, the individual's behavioral response in the presence of global information campaigns accelerate the rate of hospitalization of symptomatic individuals and also encourage the asymptomatic individuals for conducting health protocols, such as self-isolation, social distancing, etc. We calibrate the proposed model with the cumulative confirmed COVID-19 cases for the Republic of India. We estimate eight epidemiologically important parameters, and also the size of basic reproduction number for India. We find that the basic reproduction number for India is greater than unity, which represents the substantial outbreak of COVID-19 in the country. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected population. Our results reveal that to reduce disease burden in India, non-pharmaceutical interventions strategies should be implemented effectively to decrease basic reproduction number below unity. Continuous propagation of awareness through the internet and social media platforms should be regularly circulated by the health authorities/government officials for hospitalization of symptomatic individuals and quarantine of asymptomatic individuals to control the prevalence of disease in India.

Modeling the avoidance behavior of zooplankton on phytoplankton infected by free viruses.

In any ecosystem, chaotic situations may arise from equilibrium state for different reasons. To overcome these chaotic situations, sometimes the system itself exhibits some mechanisms of self-adaptability. In this paper, we explore an eco-epidemiological model consisting of three aquatic groups: phytoplankton, zooplankton, and marine free viruses. We assume that the phytoplankton population is infected by external free viruses and zooplankton get affected on consumption of infected phytoplankton; also, the infected phytoplankton do not compete for resources with the susceptible one. In addition, we model a mechanism by which zooplankton recognize and avoid infected phytoplankton, at least when susceptible phytoplankton are present. The zooplankton extinction chance increases on increasing the force of infection or decreasing the intensity of avoidance. Further, when the viral infection triggers chaotic dynamics, high zooplankton avoidance intensity can stabilize again the system. Interestingly, for high avoidance intensity, nutrient enrichment has a destabilizing effect on the system dynamics, which is in line with the paradox of enrichment. Global sensitivity analysis helps to identify the most significant parameters that reduce the infected phytoplankton in the system. Finally, we compare the dynamics of the system by allowing the infected phytoplankton also to share resources with the susceptible phytoplankton. A gradual increase of the virus replication factor turns the system dynamics from chaos to doubling state to limit cycle to stable state and the system finally settles down to the zooplankton-free equilibrium point. Moreover, on increasing the intensity of avoidance, the system shows a transcritical bifurcation from the zooplankton-free equilibrium to the coexistence steady state and remains stable thereafter.

Chaos in a nonautonomous eco-epidemiological model with delay.

In this paper, we propose and analyze a nonautonomous predator-prey model with disease in prey, and a discrete time delay for the incubation period in disease transmission. Employing the theory of differential inequalities, we find sufficient conditions for the permanence of the system. Further, we use Lyapunov's functional method to obtain sufficient conditions for global asymptotic stability of the system. We observe that the permanence of the system is unaffected due to presence of incubation delay. However, incubation delay affects the global stability of the positive periodic solution of the system. To reinforce the analytical results and to get more insight into the system's behavior, we perform some numerical simulations of the autonomous and nonautonomous systems with and without time delay. We observe that for the gradual increase in the magnitude of incubation delay, the autonomous system develops limit cycle oscillation through a Hopf-bifurcation while the corresponding nonautonomous system shows chaotic dynamics through quasi-periodic oscillations. We apply basic tools of non-linear dynamics such as Poincaré section and maximum Lyapunov exponent to confirm the chaotic behavior of the system.

Effect of active case finding on dengue control: Implications from a mathematical model.

Dengue control in India is a challenging task due to complex healthcare settings. In yesteryears, an amplification of dengue infections in India posed the need for introspection of existing dengue control policies. Prior understanding of the impacts of control interventions is necessary for their future implementation. In this paper, we propose and analyze a compartmental model of dengue to assess the impact of active case finding (ACF) on dengue disease transmission. Currently, primary prevention of dengue is possible only with vector control and personal protection from the bites of infected mosquitoes. Although a few experimental studies are performed to assess ACF in dengue disease, but this is the first attempt to represent and study the dynamics of disease using ACF as a control strategy. Local and global dynamics of the system are studied. We use sensitivity analysis to see the effects of controllable parameters of the model on the basic reproduction number and total number of infective population. We find that decrease in the biting rate of mosquitoes, and increase in the rate of hospitalization and/or notification, death rate of mosquitoes and ACF for asymptomatic and symptomatic individuals play crucial role for the reduction of disease prevalence. We calibrate our model to the yearly dengue cases in eight dengue endemic states of India. The results of our study show that ACF of symptomatic individuals will have significant effect on dengue case reduction but ACF of asymptomatic individuals cannot be ignored. Our findings indicate that the healthcare organizations must focus on ACF of symptomatic as well as asymptomatic individuals along with personal protection and mosquitoes control to achieve rapid reduction of dengue cases in India.

Fear effect in a three-species food chain model with generalist predator.

Within the framework of a food web, the foraging behavior of meso-carnivorous species is influenced by fear responses elicited by higher trophic level species, consequently diminishing the fecundity of these species. In this study, we investigate a three-species food chain model comprising of prey, an intermediate predator, and a top predator. We assume that both the birth rate and intraspecies competition of prey are impacted by fear induced by the intermediate predator. Additionally, the foraging behavior of the intermediate predator is constrained due to the presence of the top predator. It is essential to note that the top predators exhibit a generalist feeding behavior, encompassing food sources beyond the intermediate predators. The study systematically determines all feasible equilibria of the proposed model and conducts a comprehensive stability analysis of these equilibria. The investigation reveals that the system undergoes Hopf bifurcation concerning various model parameters. Notably, when other food sources significantly contribute to the growth of the top predators, the system exhibits stable behavior around the interior equilibrium. Our findings indicate that the dynamic influence of fear plays a robust role in stabilizing the system. Furthermore, a cascading effect within the system, stemming from the fear instigated by top predators, is observed and analyzed. Overall, this research sheds light on the intricate dynamics of fear-induced responses in shaping the stability and behavior of multi-species food web systems, highlighting the profound cascading effects triggered by fear mechanisms in the ecosystem.

Heme oxygenase-1 gene variants and hyperbilirubinemia risk in North Indian newborns.

Heme oxygenase-1 (HO-1) is a rate-limiting enzyme in bilirubin metabolism, and its genetic variant may modulate hyperbilirubinemia risk in neonates. The aim of the present study was to assess the association between heme oxygenase-1 gene variants and hyperbilirubinemia risk in Indian newborns. In a prospective case-control study, we analyzed (GT)n repeats and g.-413A>T variant of HO-1 gene and UGT1A1 gene variants in 100 case newborns with total serum bilirubin (TSB) levels exceeding 95th percentile and 100 control newborns with TSB levels below 75th percentile on the hour-specific bilirubin nomogram of the American Academy of Pediatrics. Study population consisted of term (37-41 weeks) and late preterm (34-36 weeks) newborns during the first 2 weeks of age. In our analysis, the (GT)n allele was highly polymorphic, ranging in number from 15 to 40. The incidence of short (GT)n allele (≤ 20) was significantly higher in neonates with hyperbilirubinemia than in controls. Although g.-413A>T variant was widely prevalent in the study population, no difference was noted in its prevalence between cases and controls. Short (GT)n repeats of HO-1 gene, c.211G>A variant of UGT1A1 gene, and excessive weight loss were independent risk factors for neonatal hyperbilirubinemia. In the presence of two or more risk factors, the odds of developing neonatal hyperbilirubinemia were high. Shorter (GT)n genotype in the promoter region of HO-1 gene is significantly associated with hyperbilirubinemia risk in Indian newborns. This genotype may interact with other genetic and clinical risk factors to further potentiate hyperbilirubinemia risk in newborns.

Investigation of a nutrient-plankton model with stochastic fluctuation and impulsive control.

In this paper, we investigate a stochastic nutrient-plankton model with impulsive control of the nutrient concentration and zooplankton population. Analytically, we find that the population size is nonnegative for a sufficiently long time. We derive some sufficient conditions for the existence of stable periodic oscillations, which indicate that the plankton populations will behave periodically. The numerical results show that the plankton system experiences a transition from extinction to the coexistence of species due to the emergence of impulsive control. Additionally, we observe that the nutrient pulse has a stronger relationship with phytoplankton growth than the zooplankton pulse. Although the frequency of impulsive control and appropriate environmental fluctuations can promote the coexistence of plankton populations, an excessive intensity of noise can result in the collapse of the entire ecosystem. Our findings may provide some insights into the relationships among nutrients, phytoplankton and zooplankton in a stochastic environment.

A systematic study of autonomous and nonautonomous predator-prey models for the combined effects of fear, refuge, cooperation and harvesting.

In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator-prey system, where the predator population is subject to harvesting at a nonlinear rate. We also focus on the effects of seasonal forcing by letting some of the model parameters to vary with time. We rigorously analyze the autonomous and nonautonomous models mathematically as well as numerically. Our simulation results show that the birth rate of prey and the fear of predators causing decline in it, and harvesting of predators first destabilize and then stabilize the system around the coexistence of prey and predator; if the birth rate of prey is very low, both prey and predator populations extinct from the ecosystem, and for a range of this parameter, only the prey population survive. The fear of predators responsible for increase in the intraspecific competition among the prey species and the refuge behavior of prey have tendency to stabilize the system, whereas the cooperative behavior of predators during the hunting time destroys stability in the ecosystem. Numerical investigations of the seasonally forced model showcase the appearances of periodic solution, higher periodic solutions, bursting patterns and chaotic dynamics.

Delay in budget allocation for vaccination and awareness induces chaos in an infectious disease model.

In this paper, we propose a model to assess the impacts of budget allocation for vaccination and awareness programs on the dynamics of infectious diseases. The budget allocation is assumed to follow logistic growth, and its per capita growth rate increases proportional to disease prevalence. An increment in per-capita growth rate of budget allocation due to increase in infected individuals after a threshold value leads to onset of limit cycle oscillations. Our results reveal that the epidemic potential can be reduced or even disease can be eradicated through vaccination of high quality and/or continuous propagation of awareness among the people in endemic zones. We extend the proposed model by incorporating a discrete time delay in the increment of budget allocation due to infected population in the region. We observe that multiple stability switches occur and the system becomes chaotic on gradual increase in the value of time delay.

Dynamics of coronavirus pandemic: effects of community awareness and global information campaigns.

The effects of social media advertisements together with local awareness in controlling COVID-19 are explored in the present investigation by means of a mathematical model. The expression for the basic reproduction number is derived. Sufficient conditions for the global stability of endemic equilibrium are obtained. We perform sensitivity analysis to identify the key parameters of the model having great impacts on the prevalence and control of COVID-19. We calibrate the proposed model to fit the data set of COVID-19 cases for India. Our simulation results show that dissemination rate of awareness among susceptible individuals at community level and individual level plays pivotal role in curtailing the COVID-19 disease. Moreover, we observe that the global information distributing from social media and local awareness coming from mouth-to-mouth communication between unaware susceptible and aware people, together with hospitalization of symptomatic individuals and quarantine of asymptomatic individuals, are much beneficial in reducing COVID-19 cases in India. Our study suggests that both global and local awareness must be implemented effectively to manage the burden of COVID-19 pandemic.

A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic.

In this paper, we propose a mathematical model to assess the impacts of using face masks, hospitalization of symptomatic individuals and quarantine of asymptomatic individuals in combating the COVID-19 pandemic in India. We calibrate the proposed model to fit the four data sets, viz. data for the states of Maharashtra, Delhi, Tamil Nadu and overall India, and estimate the rate of infection of susceptible with symptomatic population and recovery rate of quarantined individuals. We also estimate basic reproduction number to illustrate the epidemiological status of the regions under study. Our simulations infer that the infective population will be on increasing curve for Maharashtra and India, and settling for Tamil Nadu and Delhi. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected individuals. Our results reveal that to curtail the disease burden in India, specific control strategies should be implemented effectively so that the basic reproduction number is decreased below unity. The three control strategies are shown to be important preventive measures to lower disease transmission rate. The model is further extended to its stochastic counterpart to encapsulate the variation or uncertainty observed in the disease transmissibility. We observe the variability in the infective population and found their distribution at certain fixed time, which shows that for small populations, the stochasticity will play an important role.

Modeling the effect of literacy and social media advertisements on the dynamics of infectious diseases.

Education empowers humans and gets them ready to face challenges of life efficiently. Literacy and social media campaigns make people aware of the tools and techniques requisite for protection against the emerging diseases. In this paper, we investigate the combined impacts of literacy and social media on the dynamics of infectious diseases spreading through direct contact. Normalized forward sensitivity indices explore the impacts of parameters on basic reproduction number. We perform global sensitivity analysis for the infective population with respect to some controllable epidemiologically important parameters. If the growth rate of broadcasting informations through social media is very high, the system shows limit cycle oscillations. On the other hand, the baseline number of social media advertisements stabilize the system by evacuating persistent oscillations and ultimately settling the system from stable endemic equilibrium to stable disease-free state. The dissemination of awareness among literate people also suppresses the prevalence of limit cycle oscillations and drives the system to disease-free zone. An extension in model is made by assuming the growth rate of social media advertisements as periodic function of time. The simulation results show that the nonautonomous system showcases periodic as well as higher periodic solutions on the increase in the growth rate of advertisements. Our results evoke that media and education play a tremendous role in mounting awareness among the population leading to elimination of disease in the society.

Classification of Pigeonpea (Cajanus cajan (L.) Millsp.) Genotypes for Zinc Efficiency.

Pigeonpea (Cajanus cajan (L.) Millsp.) is grown globally for its protein-rich seed. However, low availability of soil zinc (Zn) adversely affects the seed yield of pigeonpea. The present study was therefore conducted to assess the Zn efficiency of pigeonpea genotypes based on seed yield and seed Zn uptake efficiency. Field experiments were conducted at the Indian Council of Agricultural Research-Indian Institute of Soil Science, Bhopal, India with twenty different pigeonpea genotypes and two levels of Zn application under a split-plot design. The two levels of Zn were low (without application of Zn fertilizer) and high (with application of 20 kg Zn ha-1 (as ZnSO4∙7H2O) as basal soil application, in conjunction with three foliar sprays of 0.50% (w/v) ZnSO4∙7H2O aqueous solution) (with 0.25% lime as neutralizing agent) at flowering, pod formation, and pod filling stages). Application of Zn improved plant height, branches plant-1, pods plant-1, seeds pod-1, and 100 seed weight of pigeonpea genotypes differently. The mean seed yield, seed Zn concentration, and seed Zn uptake of the genotypes increased from 1.71 to 2.12 t ha-1, 32.4 to 43.0 mg kg-1, and 54.9 to 90.6 g ha-1, respectively, with application of Zn. The seed yield efficiency index (SYEI) and Zn uptake efficiency index (ZUEI) of pigeonpea genotypes varied from 67.0 to 92.5 and from 47.0 to 69.9, respectively. Based on SYEI and ZUEI, the genotypes were classified as efficient and responsive (Virsa Arhar-1, GT-1, GT-101, SKNP 05-05, BDN-2, AAUT 2007-04, BSMR 853, T 15-15, DT 23, Pusa 9), efficient and non-responsive (ICPL 87119, PKV Trombay), inefficient and responsive (AKT 8811, Hisar Paras), and inefficient and non-responsive (AAUT 2007-10, JKM 7, Hisar Manak, C 11, Hisar HO2-60, GAUT 93-17). The efficient and responsive genotypes are the most useful as they yield well under low soil Zn conditions and also respond to Zn fertilizer application. The inefficient and responsive genotypes could be utilized for plant breeding programs by plant breeders for identification and utilization of responsive traits.

Effects of zooplankton selectivity on phytoplankton in an ecosystem affected by free-viruses and environmental toxins.

In the present study, we investigate the selective feeding of zooplankton on phytoplankton infected by free-viruses in the presence of environmental toxins in the marine ecosystem. The environmental toxins assume to decrease the growth rate of susceptible phytoplankton, and increase the death rate of infected phytoplankton and zooplankton. Global sensitivity analysis identifies important parameters of the system having crucial impact on the aquatic health. The coexistence equilibrium of the system stabilizes on increasing the parameters related to inhibition of phytoplankton growth due to environmental toxins and the force of infection, and destabilizes on increasing the carrying capacity of susceptible phytoplankton and preference of zooplankton on infected phytoplankton. The chance of extinction of free-viruses increases on increasing the preference of zooplankton on infected phytoplankton or decreasing the force of infection. Moreover, if the input rate of environmental toxins is high, then the system becomes zooplankton-free for higher values of force of infection. On increasing the values of preference of zooplankton on infected phytoplankton, the system exhibits transition from stable coexistence to oscillations around coexistence equilibrium to oscillations around disease-free equilibrium. We observe that the presence of free-viruses and environmental toxins in the system drive zooplankton population to very low equilibrium values but the ecological balance of the aquatic food web can be maintained by modulating the decay (depletion) rate of free-viruses (environmental toxins).

A mathematical study to control Guinea worm disease: a case study on Chad.

Global eradication of Guinea worm disease (GWD) is in the final stage but a mysterious epidemic of the parasite in dog population makes the elimination programme challenging. There is neither a vaccine nor an effective treatment against the disease and therefore intervention strategies rely on the current epidemiological understandings to control the spread of the disease. A novel mathematical model can predict the future outbreaks and it can quantify the dissemination rates of control interventions. Due to the lack of such novel models, a realistic mathematical model of GWD dynamics with human population, dog population, copepod population and the worm larvae is proposed and analyzed. Considering case data from Chad, we calibrate the model and perform global sensitivity analysis of the basic reproduction number with respect to the control parameters and copepod consumption rates. Furthermore, we investigate the impact of three control interventions: awareness of humans, isolation of infected dogs and copepod clearance from contaminated water sources. We also address the impact of combination interventions which leads to the conclusion that the combination of isolating the infected dogs and treating the contaminated ponds is a plausible way for eliminating the burden of GWD from Chad.

A simple SI-type model for HIV/AIDS with media and self-imposed psychological fear.

Infectious diseases can have a large impact on society, as they cause morbidity, mortality, unemployment, inequality and other adverse effects. Mathematical models are invaluable tools in understanding and describing disease dynamics with preventive measures for controlling the disease. The roles of media coverage and behavioral changes due to externally imposed factors on the disease dynamics are well studied. However, the effect of self-imposed psychological fear on the disease transmission has not been considered in extant research, and this gap is addressed in the present investigation. We propose a simple SI-type model for HIV/AIDS to assess the effects of media and self-imposed psychological fear on the disease dynamics. Local and global dynamics of the system are studied. Global sensitivity analysis is performed to identify the most influential parameters that have significant impact on the basic reproduction number. After calibrating our model using HIV case data-sets for Uganda and Tanzania, we calculate the basic reproduction numbers in the study period using the estimated parameters. Furthermore, a comparison of the effects of awareness and self-imposed psychological fear effects reveals that awareness is more effective in eliminating the burden of HIV infection.

Effect of diseases on symbiotic systems.

There are many species living in symbiotic communities. In this study, we analyzed models in which populations are in the mutualism symbiotic relations subject to a disease spreading among one of the species. The main goal is the characterization of symbiotic relations of coexisting species through their mutual influences on their respective carrying capacities, taking into account that this influence can be quite strong. The functional dependence of the carrying capacities reflects the fact that the correlations between populations cannot be realized merely through direct interactions, as in the usual predator-prey Lotka-Volterra model, but also through the influence of each species on the carrying capacities of the other one. Equilibria are analyzed for feasibility and stability, substantiated via numerical simulations, and global sensitivity analysis identifies the important parameters having a significant impact on the model dynamics. The infective growth rate and the disease-related mortality rate may alter the stability behavior of the system. Our results show that introducing a symbiotic species is a plausible way to control the disease in the population.

Low birthweight (LBW) and neonatal hyperbilirubinemia (NNH) in an Indian cohort: association of homocysteine, its metabolic pathway genes and micronutrients as risk factors.

BACKGROUND & AIMS: Indian subcontinent has the highest child mortality rates along with a very high frequency of low birthweight (LBW). Folate and vitamin B12 (Vit-B12) are necessary during foetal development and their deficiency prevalence in Indians is very high. The objective of the present paper is to assess whether foetal homocysteine (Hcy)/folate metabolic pathway genes, their cofactors and homocysteine level independently (or collectively) predispose children to Low birth weight. METHODS: Cord blood was collected for the study. Frequency of 5 SNPs in 4-Hcy-pathway genes, and levels of Hcy, Vit-B12 and folate were evaluated. RESULTS: Of the 421 newborns recruited for the study, 38% showed low birth weight (<2.5 kg) and 16% were preterm babies. 101 neonates developed neonatal hyperbilirubinemia (NNH). High prevalence of Vit-B12 (65%) and folate (27%) deficiency was observed in newborns along with hyperhomocystinemia (hypHcy-25%). Preterm delivery, micronutrient deficiency, hypHcy and MTHFR 677T SNP are associated as risk factor while G allele of TCN2 C776G is protective against LBW. MTHFR 677T allele and folate deficiency are also independent risk factors for NNH. CONCLUSION: We record the highest incidence of Vit-B12, folate deficiency and elevated Hcy levels, of all the studies so far reported on neonates. These together with MTHFR 677T are potential risk factors for LBW. Association of impaired folate/Hcy metabolism with NNH is reported for the first time and the possible way of interaction is discussed. It appears that proper nutritional management during pregnancy would reduce the risk of complex clinical outcomes.