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The main aim of this work is to analyze the dynamics of a delayed business cycle model described by partial differential equations (PDEs) in order to take into account the depreciation rate of capital stock and the diffusion effect.  Firstly, the existence of solutions and the economic equilibrium are carefully studied.  Secondly, the local stability and the existence of Hopf bifurcation are established.  Finally, some numerical simulations are presented to illustrate the analytical results.

This article studies a mathematical model of the fractional order of tuberculosis (TB).  It describes the dynamics of the spread of tuberculosis among smokers.  The purpose of this research is to protect vulnerable people against the virus.  According to the survey results, the required model has an equilibrium point: the disease-free equilibrium point $E_f$.  We also analyze the local stability of this equilibrium point of the model, using the basic reproduction number $\mathcal{R}_{0}$ calculated according to the new generation method.  In our model, we include three

In this paper, we suggest a diffusive and delayed IS-LM business cycle model with interest rate, general investment and money supply under homogeneous Neumann boundary conditions.  The time delays are respectively incorporated into capital stock and gross product.  We first demonstrate the model's sound mathematical and economic posing.  By examining the corresponding characteristic equation, the local stability of the economic equilibrium and the existence of Hopf bifurcation are proved.

In this paper, we delve into the analysis of an epidemic model for a vector-borne disease.

In this paper, we construct and analyse a new fishing mathematical model, which describes the time evolution of a fish stock, which is harvested by a fishing fleet, described by its fishing effort.  We consider that the price, which is given by the difference between supply and demand, is varying with respect to time.  For the harvesting function, we use the Holling II function.  On the other hand, we consider two different time scales: a fast one for the price variation and a slow one for fish stock and fishing effort variations.  We use an "aggregation of variables" m

In this paper, we propose and analyze a fractional prey–predator  model with generalized Hattaf fractional (GHF) derivative.  We prove that our proposed model is ecologically and mathematically well-posed.  Furthermore, we show that our model has three equilibrium points.  Finally, we establish the stability of these equilibria.

In this work, we present and analyze a fishery model with a price variation.  We take into account the evolution in time of the fish biomass and the harvesting effort, while the price of fish is dependent on supply and demand.  Assuming that the price variation occurs at a fast time scale.  We assume that the stock and the effort evolution follow a slow time scale.