A minimal HIV-AIDS infection model with general incidence rate and application to Morocco data

We study the global dynamics of a SICA infection model with general incidence rate. The proposed model is calibrated with cumulative cases of infection by HIV-AIDS in Morocco from 1986 to 2015. We first prove that our model is biologically and mathematically well-posed. Stability analysis of different steady states is performed and threshold parameters are identified where the model exhibits clearance of infection or maintenance of a chronic infection. Furthermore, we examine the robustness of the model to some parameter values by examining the sensitivity of the basic reproduction number. Finally, using numerical simulations with real data from Morocco, we show that the model predicts well such reality.Comment: This is a preprint of a paper whose final and definite form is with 'Statistics Opt. Inform. Comput.', Vol. 7, No 2 (2019). See [http://www.IAPress.org]. Submitted 16/Sept/2018; Revised 10 & 15/Dec/2018; Accepted 15/Dec/201

Modeling and forecasting of COVID-19 spreading by delayed stochastic differential equations

The novel coronavirus disease (COVID-19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID-19 in Morocco was reported on 2 March 2020, and the number of reported cases has increased day by day. In this work, we extend the well-known SIR compartmental model to deterministic and stochastic time-delayed models in order to predict the epidemiological trend of COVID-19 in Morocco and to assess the potential role of multiple preventive measures and strategies imposed by Moroccan authorities. The main features of the work include the well-posedness of the models and conditions under which the COVID-19 may become extinct or persist in the population. Parameter values have been estimated from real data and numerical simulations are presented for forecasting the COVID-19 spreading as well as verification of theoretical results.publishe

Economic evaluation of different cropping patterns under irrigated agriculture : a multidisciplinary approach

The purpose of this study is to determine the socioeconomic factors which influence the profitability and adoption of new cropping patterns, and to recommend suitable measures to enhance the crop diversification program in Mahaweli System B, Sri Lanka. The adoption of new cropping patterns is determined by a number of interrelated and mutually reinforcing factors. Hence, a multidisciplinary approach is used in this study to apprehend the different attributes of the new cropping patterns and farmers' decision making environment. The analytical methods include Marginal Cost-Benefit Analysis, Multivariate Analysis of Variance, Factor Analysis and Logit Probability Model. The results from the different techniques are generally in close agreement and complement each other. Results of the Marginal Cost- Benefit Analysis indicates that an increase in current crop yields and output prices may be necessary to increase the profitability of new cropping patterns to a recommendable level. Analysis of the farmers' beliefs suggests that adopters of the new cropping patterns have more positive beliefs towards the profitability and adoption of new cropping patterns when compared to nonadopters. Factor Analysis shows that there is a wide variation between the adopters and non-adopters, and also across the different locations with respect to farm-level variables. The analysis demonstrated that the information provided by 17 selected farm-level variables may be explained by four factors; namely, management factor, social factor, farm resource factor and farm stability factor. The variables highly loaded with the stability factor (number of years of residence, amount of loan obtained for farming, irrigation condition and percentage of rice produced allocated for consumption) are closely associated with the adoption rate. A logit probability model indicates that availability of farm loans significantly increases the probability of the adoption of new cropping patterns. The study results show that the crop yield, output prices, availability of farm loans and farmer beliefs, are the dominant factors which influence the adoption of new cropping patterns

Dynamics of a Stochastic Viral Infection Model with Immune Response

The aim of this work is to study the dynamical behavior of a stochastic viral infection model which is formulated by four nonlinear stochastic differential equations to describe the interactions between virus, host cells, and immune response represented by cytotoxic T lymphocytes (CTL) cells. The infection transmission process is modeled by Hattaf-Yousfi incidence function which includes many special cases existing in the literature. The positivity of solutions is investigated. In addition, the extinction of the infection is established in terms of the basic reproduction number R0. Moreover, sufficient conditions for the fluctuation of solutions around the two infection equilibria are obtained. Numerical simulations are presented to illustrate our theoretical results

Lyapunov functions and stability analysis of fractional-order systems

This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to establish the global stability of steady states for fractional-order systems and generalize some works existing in the literature. Finally, we apply our results to prove the global stability of a fractional-order SEIR model with a general incidence rate.FCTpublishe

Modeling the spread of Covid-19 pandemic in Morocco

Nowadays, coronavirus disease 2019 (Covid-19) poses a great threat to public health and economy worldwide. Unfortunately, there is yet no effective drug for this disease. For this, several countries have adopted multiple preventive interventions to avoid the spread of Covid-19. Here, we propose a delayed mathematical model to predict the epidemiological trend of Covid-19 in Morocco. Parameter estimation and sensitivity analysis of the proposed model are rigorously studied. Moreover, numerical simulations are presented in order to test the effectiveness of the preventive measures and strategies that were imposed by the Moroccan authorities and also help policy makers and public health administration to develop such strategies.FCTpublishe