The ongoing novel coronavirus epidemic was announced a pandemic by the World Health Organization on March 11, 2020, and the Government of India declared a nationwide lockdown on March 25, 2020 to ...prevent community transmission of the coronavirus disease (COVID)-19. Due to the absence of specific antivirals or vaccine, mathematical modeling plays an important role in better understanding the disease dynamics and in designing strategies to control the rapidly spreading infectious disease. In our study, we developed a new compartmental model that explains the transmission dynamics of COVID-19. We calibrated our proposed model with daily COVID-19 data for four Indian states, namely, Jharkhand, Gujarat, Andhra Pradesh, and Chandigarh. We study the qualitative properties of the model, including feasible equilibria and their stability with respect to the basic reproduction number R
. The disease-free equilibrium becomes stable and the endemic equilibrium becomes unstable when the recovery rate of infected individuals increases, but if the disease transmission rate remains higher, then the endemic equilibrium always remains stable. For the estimated model parameters, R
>1 for all four states, which suggests the significant outbreak of COVID-19. Short-time prediction shows the increasing trend of daily and cumulative cases of COVID-19 for the four states of India.
Mathematical modeling plays an important role to better understand the disease dynamics and designing strategies to manage quickly spreading infectious diseases in lack of an effective vaccine or ...specific antivirals. During this period, forecasting is of utmost priority for health care planning and to combat COVID-19 pandemic. In this study, we proposed and extended classical SEIR compartment model refined by contact tracing and hospitalization strategies to explain the COVID-19 outbreak. We calibrated our model with daily COVID-19 data for the five provinces of India namely, Kerala, Karnataka, Andhra Pradesh, Maharashtra, West Bengal and the overall India. To identify the most effective parameters we conduct a sensitivity analysis by using the partial rank correlation coefficients techniques. The value of those sensitive parameters were estimated from the observed data by least square method. We performed sensitivity analysis for R0 to investigate the relative importance of the system parameters. Also, we computed the sensitivity indices for R0 to determine the robustness of the model predictions to parameter values. Our study demonstrates that a critically important strategy can be achieved by reducing the disease transmission coefficient βs and clinical outbreak rate qa to control the COVID-19 outbreaks. Performed short-term predictions for the daily and cumulative confirmed cases of COVID-19 outbreak for all the five provinces of India and the overall India exhibited the steady exponential growth of some states and other states showing decays of daily new cases. Long-term predictions for the Republic of India reveals that the COVID-19 cases will exhibit oscillatory dynamics. Our research thus leaves the option open that COVID-19 might become a seasonal disease. Our model simulation demonstrates that the COVID-19 cases across India at the end of September 2020 obey a power law.
COVID-19 is an infectious disease caused by the SARS-CoV-2 virus that first appeared in Wuhan city and then globally. The COVID-19 pandemic exudes public health and socio-economic burden globally. ...Mathematical modeling plays a significant role to comprehend the transmission dynamics and controlling factors of rapid spread of the disease. Researchers focus on the human-to-human transmission of the virus but the SARS-CoV-2 virus also contaminates the environment. In this study we proposed a nonlinear mathematical model for the COVID-19 pandemic to analyze the transmission dynamics of the disease in India. We have also incorporated the environment contamination by the infected individuals as the population density is very high in India. The model is fitted and parameterized using daily new infection data from India. Analytical study of the proposed COVID-19 model, including feasibility of critical points and their stability reveals that the infection-free steady state is stable if the basic reproduction number is less than unity otherwise the system shows significant outbreak. Numerical illustrations demonstrates that if the rate of environment contamination increased then the number of infected persons also increased. But if the environment is disinfected by sanitization then the number of infected persons cannot drastically increase.
•A predator-prey model incorporating the cost of fear into prey reproduction.•Strong anti-predator responses can stabilize the predator-prey system by excluding the existence of periodic ...solutions.•Model undergoes Hopf bifurcation with respect to prey birth rate r0.•Fear effect can stabilize the predator-prey system and promote the coexistence of all the populations.•Prey is less sensitive to perceive predation risk with increasing birth rate of prey or increasing death rate of predators.
Several field data and experiments on a terrestrial vertebrates exhibited that the fear of predators would cause a substantial variability of prey demography. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. Based on the experimental evidence, we proposed and analyzed a prey-predator system introducing the cost of fear into prey reproduction with Holling type-II functional response. We investigate all the biologically feasible equilibrium points, and their stability is analyzed in terms of the model parameters. Our mathematical analysis exhibits that for strong anti-predator responses can stabilize the prey-predator interactions by ignoring the existence of periodic behaviors. Our model system undergoes Hopf bifurcation by considering the birth rate r0 as a bifurcation parameter. For larger prey birth rate, we investigate the transition to a stable coexisting equilibrium state, with oscillatory approach to this equilibrium state, indicating that the greatest characteristic eigenvalues are actually a pair of imaginary eigenvalues with real part negative, which is increasing for r0. We obtained the conditions for the occurrence of Hopf bifurcation and conditions governing the direction of Hopf bifurcation, which imply that the prey birth rate will not only influence the occurrence of Hopf bifurcation but also alter the direction of Hopf bifurcation. We identify the parameter regions associated with the extinct equilibria, predator-free equilibria and coexisting equilibria with respect to prey birth rate, predator mortality rates. Fear can stabilize the predator-prey system at an interior steady state, where all the species can exists together, or it can create the oscillatory coexistence of all the populations. We performed some numerical simulations to investigate the relationship between the effects of fear and other biologically related parameters (including growth/decay rate of prey/predator), which exhibit the impact that fear can have in prey-predator system. Our numerical illustrations also demonstrate that the prey become less sensitive to perceive the risk of predation with increasing prey growth rate or increasing predators decay rate.
In this study, we investigate a mathematical model that describes the interactive dynamics of a predator-prey system with different kinds of response function. The positivity, boundedness, and ...uniform persistence of the system are established. We investigate the biologically feasible singular points and their stability analysis. We perform a comparative study by considering different kinds of functional responses, which suggest that the dynamical behavior of the system remains unaltered, but the position of the bifurcation points altered. Our model system undergoes Hopf bifurcation with respect to the growth rate of the prey population, which indicates that a periodic solution occurs around a fixed point. Also, we observed that our predator-prey system experiences transcritical bifurcation for the prey population growth rate. By using normal form theory and center manifold theorem, we investigate the direction and stability of Hopf bifurcation. The biological implications of the analytical and numerical findings are also discussed in this study.
•A diffusive predator-prey system with the effect of fear due to predator population.•Performed qualitative properties of model, including positivity, boundedness, existence of steady states and ...their local stability, transcritical and Hopf bifurcation.•We explored how behavioral modification in prey species due to fear of predator and mutual interference between predators can create different spatiotemporal patterns in population distribution.•In case of diffusive system, we provide a detailed stability analysis and obtain the conditions for Turing instability.•Our simulation results reveal that the diffusion-driven instability creates various spatio-temporal patterns including warm spot pattern for three different initial data.
Recent field experiments on vertebrates show that though mere presence of a predator causes a dramatic change in prey demography, the fear of predators increases the survival probability of prey leading to a cost of prey production. Based on the experimental findings, we proposed and analyzed a mathematical model that incorporates the fear-induced birth reduction in the prey population due to presence of predator. A modified and more realistic fear function is proposed in this study. Qualitative behavior of the model is performed including positivity and boundedness of solutions, existence of critical points and their local stability analysis, existence of transcritical and Hopf bifurcation. We analyzed Hopf bifurcation with respect to the prey growth rate and the level of fear. Transcritical bifurcation is analyzed by varying the prey growth rate. Distribution of the population of interacting species in a large scale natural system is heterogeneous and subject to alter for different reasons. Thus, we investigate how behavioral modification in prey population due to fear for predators and mutual interference among predator species can create various spatiotemporal pattern formation in population distribution. In the spatially extended system, we provide a detailed stability analysis and obtain the conditions for Turing instability. Numerical simulations are performed to validate analytical results for both non-spatial and spatial models. Warm spot patterns are obtained by considering three different types of initial data and discussed the biological significance of these patterns for the two-dimensional spatial model. Our numerical simulation demonstrates that the fear effect in a diffusive predator-prey system with mutual interference between predators may exhibit more complicated dynamics.
•We propose a SARIIqSq compartmental mathematical model that explains the transmission dynamics of COVID-19.•Perform PRCC analysis to identify the most sensitive parameters and the sensitive ...parameters are estimated based on the real data up to April 30, 2020.•A sensitivity analysis is conducted to identify the most effective parameters with respect to the basic reproduction number R0.•Model simulation demonstrates that the eradication of COVID-19 is possible by mitigating the disease transmission rate βs.•Based on the estimated data our model predicts end dates of COVID-19 for 17 provinces of India and overall India.
In India, 100,340 confirmed cases and 3155 confirmed deaths due to COVID-19 were reported as of May 18, 2020. Due to absence of specific vaccine or therapy, non-pharmacological interventions including social distancing, contact tracing are essential to end the worldwide COVID-19. We propose a mathematical model that predicts the dynamics of COVID-19 in 17 provinces of India and the overall India. A complete scenario is given to demonstrate the estimated pandemic life cycle along with the real data or history to date, which in turn divulges the predicted inflection point and ending phase of SARS-CoV-2. The proposed model monitors the dynamics of six compartments, namely susceptible (S), asymptomatic (A), recovered (R), infected (I), isolated infected (Iq) and quarantined susceptible (Sq), collectively expressed SARIIqSq. A sensitivity analysis is conducted to determine the robustness of model predictions to parameter values and the sensitive parameters are estimated from the real data on the COVID-19 pandemic in India. Our results reveal that achieving a reduction in the contact rate between uninfected and infected individuals by quarantined the susceptible individuals, can effectively reduce the basic reproduction number. Our model simulations demonstrate that the elimination of ongoing SARS-CoV-2 pandemic is possible by combining the restrictive social distancing and contact tracing. Our predictions are based on real data with reasonable assumptions, whereas the accurate course of epidemic heavily depends on how and when quarantine, isolation and precautionary measures are enforced.
Situated in the eastern coastal state of West Bengal, the Sundarbans Estuarine System (SES) is India’s largest monsoonal, macro-tidal delta-front estuarine system. It comprises the southernmost part ...of the Indian portion of the Ganga–Brahmaputra delta bordering the Bay of Bengal. The Sundarbans Estuarine Programme (SEP), conducted during 18–21 March 2011 (the Equinoctial Spring Phase), was the first comprehensive observational programme undertaken for the systematic monitoring of the tides within the SES. The 30 observation stations, spread over more than 3600 km
2
, covered the seven inner estuaries of the SES (the Saptamukhi, Thakuran, Matla, Bidya, Gomdi, Harinbhanga, and Raimangal) and represented a wide range of estuarine and environmental conditions. At all stations, tidal water levels (every 15 minutes), salinity, water and air temperatures (hourly) were measured over the six tidal cycles. We report the observed spatio-temporal variations of the tidal water level. The predominantly semi-diurnal tides were observed to amplify northwards along each estuary, with the highest amplification observed at Canning, situated about 98 km north of the seaface on the Matla. The first definite sign of decay of the tide was observed only at Sahebkhali on the Raimangal, 108 km north of the seaface. The degree and rates of amplification of the tide over the various estuarine stretches were not uniform and followed a complex pattern. A least-squares harmonic analysis of the data performed with eight constituent bands showed that the amplitude of the semi-diurnal band was an order of magnitude higher than that of the other bands and it doubled from mouth to head. The diurnal band showed no such amplification, but the amplitude of the 6-hourly and 4-hourly bands increased headward by a factor of over 4. Tide curves for several stations displayed a tendency for the formation of double peaks at both high water (HW) and low water (LW). One reason for these double-peaks was the HW/LW stands of the tide observed at these stations. During a stand, the water level changes imperceptibly around high tide and low tide. The existence of a stand at most locations is a key new finding of the SEP. We present an objective criterion for identifying if a stand occurs at a station and show that the water level changed imperceptibly over durations ranging from 30 minutes to 2 hours during the tidal stands in the SES. The tidal duration asymmetry observed at all stations was modified by the stand. Flow-dominant asymmetry was observed at most locations, with ebb-dominant asymmetry being observed at a few locations over some tidal cycles. The tidal asymmetry and stand have implications for human activity in the Sundarbans. The longer persistence of the high water level around high tide implies that a storm surge is more likely to coincide with the high tide, leading to a greater chance of destruction. Since the stands are associated with an amplification of the 4-hourly and 6-hourly constituents, storm surges that have a similar period are also likely to amplify more during their passage through the SES.
We use 14 years of satellite-derived sea-surface temperature (SST) data to compute a monthly frontal probability index (FPI) to determine the existence of a front in a pixel. A persistent SST front ...is deemed to exist if the FPI in a narrow region exceeds that in the surrounding ocean. We describe the seasonal variability of 17 persistent SST fronts (eight associated with the shelf-slope boundary and five with the mixing between different water masses) in the north Indian Ocean. Only weak fronts exist during a few months in the strong upwelling regimes off Somalia and Oman.
We used satellite-derived sea-surface-temperature (SST) data along with in-situ data collected along a meridional transect between 18.85 and 20.25°N along 69.2°E to describe the evolution of an SST ...filament and front during 25 November to 1 December in the northeastern Arabian Sea (NEAS). Both features were ~100km long, lasted about a week, and were associated with weak temperature gradients (~0.07°Ckm−1). The in-situ data were collected first using a suite of surface sensors during a north–south mapping of this transect and showed the existence of a chlorophyll maximum within the filament. This surface data acquisition was followed by a high-resolution south–north CTD (conductivity–temperature–depth) sampling along the transect. In the two days that elapsed between the two in-situ measurements, the filament had shrunk in size and moved northward. In general, the current direction was northwestward and advected these mesoscale features. The CTD data also showed an SST front towards the northern end of the transect. In both these features, the chlorophyll concentration was higher than in the surrounding waters. The temperature and salinity data from the CTD suggest upward mixing or pumping of water from the base of the mixed layer, where a chlorophyll maximum was present, into the mixed layer that was about 60m thick. A striking diurnal cycle was evident in the chlorophyll concentration, with higher values tending to occur closer to the surface during the night. The in-situ data from both surface sensors and CTD, and so also satellite-derived chlorophyll data, showed higher chlorophyll concentration, particularly at sub-surface levels, between the filament and the front, but there was no corresponding signature in the temperature and salinity data. Analysis of the SST fronts in the satellite data shows that fronts weaker than those associated with the filament and the front had crossed the transect in this region a day or two preceding the sampling of the front.
•We use satellite SST and in-situ measured data to describe a filament/front.•These features were ~100km long, lasted about a week.•They were associated with weak temperature gradients and high chlorophyll.•These mesoscale features were advected by the current.•Upward mixing of water from the base of the MLD was evident from CTD data.
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