A stochastic SICA epidemic model for HIV transmission

We propose a stochastic SICA epidemic model for HIV transmission, described by stochastic ordinary differential equations, and discuss its perturbation by environmental white noise. Existence and uniqueness of the global positive solution to the stochastic HIV system is proven, and conditions under which extinction and persistence in mean hold, are given. The theoretical results are illustrated via numerical simulations.Comment: This is a preprint of a paper whose final and definite form is with 'Applied Mathematics Letters', ISSN 0893-9659. Submitted 22/Jan/2018; Revised 03/May/2018; Accepted for publication 03/May/201

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

STOCHASTIC MODEL ANALYSIS OF THE IMPACT OF MEDIA CAMPAIGN ON TRANSMISSION OF COVID – 19 EPIDEMIC.

The COVID - 19 pandemic is currently causing authorities and public health officials more concern. The goal of the project is to convert a deterministic model for COVID-19 transmissions to a stochastic model, and then analyze the results to see how media-driven awareness campaigns have an impact on the disease's spread. The dynamic COVID-19 model was converted to a stochastic model, which was then examined. The model includes the following categories: Susceptible (S), Exposed (E), Infected class (I),  Isolated class ( ), Aware class  and Recovered class (R), as well as the Cumulative density of awareness programs by media denoted by   . With the help of MATLAB, the converted model is then numerically solved using the Eula Maruyama approach, allowing the existence and uniqueness of the model to be examined. The implementation of awareness programs has been found to have a significant positive impact on the spread of COVID-19. As the rate of implementation of these programs rises, the population that is exposed to the virus and those who are infected with it declines, and it has been hypothesized that this will eventually cause COVID-19 to become extinct. According to the report, putting awareness campaigns into place can help stop the COVID-19 epidemic from spreading

Near-optimal control of a stochastic SICA model with imprecise parameters

An adequate near-optimal control problem for a stochastic SICA (Susceptible-Infected-Chronic-AIDS) compartmental epidemic model for HIV transmission with imprecise parameters is formulated and investigated. We prove some estimates for the state and co-state variables of the stochastic system. The established inequalities are then used to prove a necessary and a sufficient condition for near-optimal control with imprecise parameters. The proofs involve several mathematical and stochastic tools, including the Burkholder-Davis-Gundy inequality.Portuguese Foundation for Science and Technology (FCT) and UIDB/04106/2020 (CIDMA).publishe

Mathematical analysis, forecasting and optimal control of HIV/AIDS spatiotemporal transmission with a reaction diffusion SICA model

We propose a mathematical spatiotemporal epidemic SICA model with a control strategy. The spatial behavior is modeled by adding a diffusion term with the Laplace operator, which is justified and interpreted both mathematically and physically. By applying semigroup theory on the ordinary differential equations, we prove existence and uniqueness of the global positive spatiotemporal solution for our proposed system and some of its important characteristics. Some illustrative numerical simulations are carried out that motivate us to consider optimal control theory. A suitable optimal control problem is then posed and investigated. Using an effective method based on some properties within the weak topology, we prove existence of an optimal control and develop an appropriate set of necessary optimality conditions to find the optimal control pair that minimizes the density of infected individuals and the cost of the treatment program

Transmission dynamics of symptom-dependent HIV/AIDS models

In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators Rs0 and Re0 were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted