Dynamic analysis and control of a rice-pest system under transcritical bifurcations.

A decision model is developed by adopting two control techniques, combining cultural methods and pesticides in a hybrid approach. To control the adverse effects in the long term and to be able to evaluate the extensive use of pesticides on the environment and nearby ecosystems, the novel decision model assumes the use of pesticides only in an emergency situation. We, therefore, formulate a rice-pest-control model by rigorously modelling a rice-pest system and including the decision model and control techniques. The model is then extended to become an optimal control system with an objective function that minimizes the annual losses of rice by controlling insect pest infestations and simultaneously reduce the adverse impacts of pesticides on the environment and nearby ecosystems. This rice-pest-control model is verified by analysis, obtains the necessary conditions for optimality, and confirms our main results numerically. The rice-pest system is verified by stability analysis at equilibrium points and shows transcritical bifurcations indicative of acceptable thresholds for insect pests to demonstrate the pest control strategy.

Modeling the optimal mitigation of potential impact of climate change on coastal ecosystems.

Global warming is adversely affecting the earth's climate system due to rapid emissions of greenhouse gases (GHGs). Consequently, the world's coastal ecosystems are rapidly approaching a dangerous situation. In this study, we formulate a mathematical model to assess the impact of rapid emissions of GHGs on climate change and coastal ecosystems. Furthermore, we develop a mitigation method involving two control strategies: coastal greenbelt and desulfurization. Here, greenbelt is considered in coastal areas to reduce the concentrations of GHGs by absorbing the environmental carbon dioxide (CO2), whereas desulfurization is considered in factories and industries to reduce GHG emissions by controlling the release of harmful sulfur compounds. The model and how it can control the situation are analytically verified. Numerical results of this study are confirmed by comparison with other studies that examine different scenarios. Results show that both control strategies can mitigate GHG concentrations, curtail global warming and to some extent manage climate change. The results further reveal that both control strategies are more effective than one control method. Overall, the results suggest that the concentrations of GHGs and the effects of climate change can be controlled by adopting sufficient coastal greenbelt and desulfurization techniques in various industries.

Modeling the dispersal effect to reduce the infection of COVID-19 in Bangladesh.

In this paper, we propose a four compartmental model to understand the dynamics of infectious disease COVID-19. We show the boundedness and non-negativity of solutions of the model. We analytically calculate the basic reproduction number of the model and perform the stability analysis at the equilibrium points to understand the epidemic and endemic cases based on the basic reproduction number. Our analytical results show that disease free equilibrium point is asymptotically stable (unstable) and endemic equilibrium point is unstable (asymptotically stable) if the basic reproduction number is less than (greater than) unity. The dispersal rate of the infected population and the social awareness control parameter are the main focus of this study. In our model, these parameters play a vital role to control the spread of COVID-19. Our results reveal that regional lockdown and social awareness (e.g., wearing a face mask, washing hands, social distancing) can reduce the pandemic of the current outbreak of novel coronavirus in a most densely populated country like Bangladesh.