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The dynamics of infectious disease transmission depends on social contact patterns and the precautions people take to minimize disease transmission. The social contact pattern varies depending on the community at large age distribution at work, school, and recreation. Consequently, knowing the age-specific prevalence and incidence of infectious diseases is critical for predicting future disease burden and the efficacy of interventions like vaccination. In this study, we use an SEIR age-structured multi-group epidemic model to understand how social contact affects disease control. We construct location-specific social contact matrices to observe that how social mixing affects disease spread. For mathematical analysis, we compute the basic reproduction number (R 0) and exhibit the global behavior of the system in terms of R 0 . We also estimate the transmission rate using the empirical data of COVID-19 for India from 1 September 2020, to 31 December 2020. We simulate the lifting of non-pharmaceutical interventions by allowing people to return to work in phases and investigate its impact. Our findings imply that raising awareness in symptomatic infected individuals aged 20–49 years can help in reducing the number of infected individuals. When some schools are partially open, awareness in symptomatic infected individuals in school-age groups also plays a significant role in reducing disease cases. The simulation results also suggest that limiting contact at school and other gathering places could significantly lower the number of instances. Using the least square approach, we show that the time-dependent transmission rate is more realistic than the constant spread rate for COVID-19 in India. To reduce the COVID-19 burden, we obtain that gradually loosening control measures could flatten and lower other peaks. Our findings may help health policymakers to decide on timely age-based vaccination distribution strategies and control measures. [ABSTRACT FROM AUTHOR]

The Zika virus (ZIKV) epidemic is depicted to have high spatial diversity and slow growth, attributable to the dynamics of the mosquito vector and mobility of the human populations. In an effort to understand the transmission dynamics of Zika virus, we formulate a new compartmental epidemic model with a system of seven differential equations and 11 parameters incorporating the decaying transmission rate and study the impact of protection measure on basic public health. We do not fit the model to the observed pattern of spread, rather we use parameter values estimated in the past and examine the extent to which the designed model prediction agrees with the pattern of spread seen in Brazil, via reaction–diffusion modeling. Our work includes estimation of key epidemiological parameters such as basic reproduction number ( R 0) , and gives a rough estimate of how many individuals can be typically infected during an outbreak if it occurs in India. We used partial rank correlation coefficient method for global sensitivity analysis to identify the most influential model parameters. Using optimal control theory and Pontryagin's maximum principle, a control model has been proposed and conditions for the optimal control are determined for the deterministic model of Zika virus. The control functions for the strategies (i) vector-to-human contact reduction and (ii) vector elimination are introduced into the system. Numerical simulations are also performed. This work aimed at understanding the potential extent and timing of the ZIKV epidemic can be used as a template for the analysis of future mosquito-borne epidemics. [ABSTRACT FROM AUTHOR]

In this paper, we have formulated a compartmental epidemic model with exponentially decaying transmission rates to understand the Ebola transmission dynamics and study the impact of control measures to basic public health. The epidemic model exhibits two equilibria, namely, the disease-free and unique endemic equilibria. We have calculated the basic reproduction number through next generation matrix and investigated the spatial spread of the epidemic via reaction-diffusion modeling. Instead of fitting the model to the observed pattern of spread, we have used previously estimated parameter values and examined the efficacy of predictions of the designed model vis-à-vis the pattern of spread observed in Sierra Leone, West Africa. Further, we conducted a sensitivity analysis to determine the extent to which improvement in predictions is achievable through better parameterization. We performed numerical simulations with and without control measure for the designed model system. A significant reduction in infection and death cases were observed when proper control measures are incorporated in the model system. Two-dimensional simulation experiments show that infectious population and the number of deaths will increase up to one and a half years without control, but it will decline after two years. We have reported the numerical results, and it closely matches with the real situation in Sierra Leone. [ABSTRACT FROM AUTHOR]

The bloom of toxin producing phytoplankton (TPP) is an environmental issue due to its negative impact on fresh water and marine ecology. In this paper, such a phenomenon is modeled using the reaction-diffusion equations. The spatiotemporal interaction among non-toxin producing phytoplankton (NTP), TPP, and zooplankton has been considered with Holling type II and III functional responses. The stability analysis for non-spatial and spatial model system is carried out and numerical simulations are performed for a fixed set of parameter values, which is realistic to planktonic dynamics. It has been observed that on increasing the reduction rate of zooplankton, the system shows cyclic to stable behavior. The result shows that the predators which avoid to toxic prey promote the bloom. Non-Turing patchy pattern has also been observed on time evolution. In this work, we have taken the case study of Sundarban mangrove wetland which is suffering from algal bloom due to the presence of toxic Dinoflagellates and Cyanophyceae. Through the numerical simulation, it has been shown that the higher value of reduction rate of zooplankton () is responsible for bad health of the wetland system. [ABSTRACT FROM AUTHOR]

In this paper, the complex dynamics of a spatial aquatic system in the presence of self- and cross-diffusion are investigated. Criteria for local stability, instability and global stability are obtained. The effect of critical wavelength which can drive a system to instability is investigated. We noticed that cross-diffusion coefficient can be quite significant, even for small values of off-diagonal terms in the diffusion matrix. With the help of numerical simulation, we observed the Turing patterns (spots, strips, spot-strips mixture), regular spiral patterns and irregular patchy structures. The beauty and complexity of the Turing patterns are attributed to a large variety of symmetry properties realized by different values of predator's immunity, rate of fish predation and half saturation constant of predator population. [ABSTRACT FROM AUTHOR]

An attempt has been made to introduce the mathematical modeling of nonlinear non-equilibrium spatio-temporal pattern formation in a minimal model of a spatial aquatic system. A hybrid model of the spatio-temporally continuous phytoplankton-zooplankton system with Holling type IV predator response but discrete agents like fish dynamics has been presented. The model has been investigated for plankton patch formation, which is known from natural plankton populations. Fish predation has a significant role in the temporal evolution of spatial pattern of phytoplankton-zooplankton system, which suggests that unstable diffusive system can be made stable by increasing the rate of fish predation and diffusivity constant to sufficiently large values. [ABSTRACT FROM AUTHOR]