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Cholera is a waterborne disease that continues to pose serious public health problems in many developing countries. Increasing water and sanitation coverage is a goal for local authorities in these countries, as it can eliminate one of the root causes of cholera transmission. The SIWDR (susceptible–infected–water–dumpsite–recovered) model is proposed here to evaluate the effects of the improved coverage of water and sanitation services in a community at risk of a cholera outbreak. This paper provides a mathematical study of the dynamics of the water and sanitation (WatSan) deficits and their public health impact in a community. The theoretical analysis of the SIWDR model gave a certain threshold value (known as the basic reproductive number and denoted R 0 ) to stop the transmission of cholera. It was found that the disease-free equilibrium was globally asymptotically stable whenever R 0 ≤ 1 . The unique endemic equilibrium was globally asymptotically stable whenever R 0 > 1 . Sensitivity analysis was performed to determine the relative importance of model parameters to disease transmission and prevention. The numerical simulation results, using realistic parameter values in describing cholera transmission in Haiti, showed that improving the drinking water supply, wastewater and sewage treatment, and solid waste disposal services would be effective strategies for controlling the transmission pathways of this waterborne disease. [ABSTRACT FROM AUTHOR]

Ecological stoichiometry is the study of the balance of multiple elements in ecological interactions and processes (Sterner and Elser in Ecological Stoichiometry: The Biology of Elements from Molecules to the Biosphere, 2002). Modeling under this framework enables us to investigate the effect nutrient content on organisms whether the imbalance involves insufficient or excess nutrient content. This phenomenon is called the "stoichiometric knife-edge". In this paper, a discrete-time predator–prey model that captures this phenomenon is established and qualitatively analyzed. We systematically expound the similarities and differences between our discrete model and the corresponding continuous analog. Theoretical and numerical analyses show that while the discrete and continuous models share many properties, differences also exist. Under certain parameter sets, the models exhibit qualitatively different dynamics. While the continuous model shows limit cycle, Hopf bifurcation, and saddle-node bifurcation, the discrete-time model exhibits richer dynamical behaviors, such as chaos. By comparing the dynamics of the continuous and discrete model, we can conclude that stoichiometric effects of low food quality on predators are robust to the discretization of time. This study can possibly serve as an example for pointing to the importance of time scale in ecological modeling. [ABSTRACT FROM AUTHOR]

Acknowledging many effects on humans, which are ignored in deterministic models for COVID-19, in this paper, we consider stochastic mathematical model for COVID-19. Firstly, the formulation of a stochastic susceptible–infected–recovered model is presented. Secondly, we devote with full strength our concentrated attention to sufficient conditions for extinction and persistence. Thirdly, we examine the threshold of the proposed stochastic COVID-19 model, when noise is small or large. Finally, we show the numerical simulations graphically using MATLAB. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some new nonlinear dynamic integral inequalities containing integration on infinite interval on time scales, which provide explicit bounds on unknown functions. Our results not only generalize some dynamic inequalities in related literature, but also are new even for the continuous and discrete time cases. Two examples are given to illustrate the present results. [ABSTRACT FROM AUTHOR]

This manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentioned model is considered with a nonsingular kernel type derivative given by Caputo–Fabrizo with fractional order. For the required results of the existence and uniqueness of solution to the proposed model, Picard's iterative method is applied. Furthermore, to investigate approximate solutions to the proposed model, we utilize the Laplace transform and Adomian's decomposition (LADM). Some graphical presentations are given for different fractional orders for various compartments of the model under consideration. [ABSTRACT FROM AUTHOR]

A disastrous coronavirus, which infects a normal person through droplets of infected person, has a route that is usually by mouth, eyes, nose or hands. These contact routes make it very dangerous as no one can get rid of it. The significant factor of increasing trend in COVID19 cases is the crowding factor, which we named "crowding effects". Modeling of this effect is highly necessary as it will help to predict the possible impact on the overall population. The nonlinear incidence rate is the best approach to modeling this effect. At the first step, the model is formulated by using a nonlinear incidence rate with inclusion of the crowding effect, then its positivity and proposed boundedness will be addressed leading to model dynamics using the reproductive number. Then to get the graphical results a nonstandard finite difference (NSFD) scheme and fourth order Runge–Kutta (RK4) method are applied. [ABSTRACT FROM AUTHOR]

Since Kermack and McKendrick have introduced their famous epidemiological SIR model in 1927, mathematical epidemiology has grown as an interdisciplinary research discipline including knowledge from biology, computer science, or mathematics. Due to current threatening epidemics such as COVID-19, this interest is continuously rising. As our main goal, we establish an implicit time-discrete SIR (susceptible people–infectious people–recovered people) model. For this purpose, we first introduce its continuous variant with time-varying transmission and recovery rates and, as our first contribution, discuss thoroughly its properties. With respect to these results, we develop different possible time-discrete SIR models, we derive our implicit time-discrete SIR model in contrast to many other works which mainly investigate explicit time-discrete schemes and, as our main contribution, show unique solvability and further desirable properties compared to its continuous version. We thoroughly show that many of the desired properties of the time-continuous case are still valid in the time-discrete implicit case. Especially, we prove an upper error bound for our time-discrete implicit numerical scheme. Finally, we apply our proposed time-discrete SIR model to currently available data regarding the spread of COVID-19 in Germany and Iran. [ABSTRACT FROM AUTHOR]