The paper studies the dynamics of a full delay-logistic population model incorporated with a proportionate harvesting function. The study discusses the stability of the model in comparison with the well-known Hutchinson logistic growth equation with harvesting function using the rate of harvesting as a bifurcation parameter to determine sustainable harvesting rate even at a bigger time delay of . In all cases, the Hutchinson equation with harvesting was forced to converge to equilibrium using an additional and a different time delay parameter, a deficiency previous researchers have failed to address when the Hutchinson model is used for this purpose. The population fluctuations are catered for with this model making the estimated maximum sustainable growth and harvest reflect realities as this model drastically reduces time-delay associated oscillations compared to the well-known Hutchinson delayed logistic models. The numerical simulations were be done using the MatLab Software.

The paper uses a new technique to find a unique solution to a delay differential cobweb model (formulated from a joint supply-demand function of price) with real model parameters via the Lambert W-function without considering any complex branches. The dynamics of the model are demonstrated with simulations and found to complement previous studies using literature values. However, the condition for instability in the previous studies was defied by our model due to the time delay associated with the supply function. The practical application and advantage of this model over the existing models are that the stability of this model is not limited to only the ratio of price elasticity of demand and supply but also the time-delay parameter (i.e., a missing link in the previous models). Our model, on the other hand, loses its stability when the time delay associated with the supply function is fixed at . Since most of the physical systems, including economical systems, are time-delay inherent and such stability conditionalities should not limit their performance, it is recommended that such systems be modelled using delay differential functions. The novelty of this research is that there has not been a definite general solution to the cobweb model with a time delay whose price dynamics mimic the behaviour of the existing cobweb models in the literature. An illustrative example in a delayed fractional-order differential equation also buttressed the importance of the time delay in the model, aside from the impact of the ratio of the price elasticity of supply and demand.

The paper examines the fish population dynamics of a delay logistic model with restrictions on harvesting in a deterministic environment. This is the first time an autonomous model with a harvesting function has been created to regulate the harvesting of fish. The goal of the study is to help external regulatory bodies manage fishing harvests and replenish fish stocks. The dynamics scenario mirrors the facts of fishing systems and enhances the research that has already been done. Two restriction conditions are employed. In the event that the agency detects overfishing, all fish harvesting is prohibited, with the fishing control parameter raised in order to bring the fish back to full stock, while the catchability coefficient is set to zero. However, if the system is designed so that harvesting is carried out in accordance with the fish’s sustainable growth level, then we have the partial restriction condition where no ban is imposed on fishing. This model’s practical benefit is its adaptability; it may be redesigned to suit any physical system whose functioning is comparable to this phenomenon. As a result, it is advised that the regulatory bodies use the model to manage the fish stock.

This paper deals with the stability and occurrence of Hopf bifurcation of a distributed delay differential cobweb model using the chain trick technique. This is a generalized form of the fixed delay cobweb model to which it is compared using the same parameter values. The results from the delay distribution showed that whenever less weight $(\gamma =0.146)$ is put on past prices, the current equilibrium price is adjusted upwards while the reverse is observed when a higher weight $(\gamma =0.186)$ is put on the previous price. It is also observed that if the initial price is set below/above the equilibrium price, the price adjustment either affects the consumers or benefits the suppliers. However, the fixed delay cobweb model does not display the consumers or suppliers benefits of the price dynamics in either direction. These are unique, underlying patterns in price dynamics discovered when using a distributed delay model compared to traditional fixed delay cobweb models. Furthermore, our model challenges the traditional cobweb model’s requirement for divergence, as it is based on the weight assigned to past prices rather than the relationship between the elasticities of supply and demand, which is the determining factor in the classical model. Based on these insights, we recommend that future price adjustment models incorporate distributed delays, as they reveal more intricate price dynamics and provide a more comprehensive understanding of market behavior than fixed delay models.

The knowledge of economic and financial indicators is the basis of making right decisions and sound judgment with respect to investment and allocation scare of resources. Such important indicators include the consumer price index, which measures the change in the prices paid by households for goods and services consumed. A trigger in the consumer price in Ghana causes inflation which affects the purchasing power of its citizens. Knowledge of the trend of the CPI is crucial in economic planning. The study therefore sought to construct the appropriate time series model for the CPI and then use the model to predict the next nine months CPI. The study further sought to determine the type of trend model that characterizes the CPI. The Box-Jenkins methodology was adopted. The results of analysis showed SARIMA(2, 1, 1)(1, 0, 0)₁₂ as most fitted time series model and was used to predict the consumer price index for the next nine months. The S-model was also found to be the appropriate trend model for the CPI. The SARIMA (2, 1, 1)(1, 0, 0)₁₂ is recommended for forecasting consumer price index in Ghana.

This study compares the price dynamics of a Caputo fractional order delay differential cobweb model with existing cobweb models that have conformable fractional derivatives, Caputo fractional derivatives, and nonsingular kernel fractional derivatives to determine the effect of the time delay parameter on commodity price, besides the positivity of the solution that was investigated. In contrast to previous research, the stability study shows the practical usefulness of our model since the literature’s various time intervals showed short‐term equilibrium price convergence but long‐term price divergence. The results showed that the time gap between supply and demand accounts for the noise associated with the fractional‐order time delay differential cobweb regarding convergence (or divergence), which is nonexistent in the literature models. It is observed in the paper that lower fractional order goes with a higher time delay, while we have the reverse for high fractional order. This depicts the realities of price behaviour in connection with the law of demand and supply of commodities that take a finite period for them to be ready for distribution to the market. It is, therefore, recommended that price adjustment models be modeled using fractional delay differential equations. The numerical simulations were done using MATLAB.