A novel approach to model the role of mobility suppression and vaccinations in containing epidemics in a network of cities.

This paper presents a comprehensive agent-based model for the spread of an infection in a network of cities. Directional mobility is defined between each two cities and can take different values. The work examines the role that such mobility levels play in containing the infection with various vaccination coverage and age distributions. The results indicate that mobility reduction is sufficient to control the disease under all circumstances and full lockdowns are not a necessity. It has to be reduced to different ratios depending on the vaccination level and age distribution. A key finding is that increasing vaccination coverage above a certain level does not affect the mobility suppression level required to control the infection anymore for the cases of young population and heterogeneous age distributions. By investigating several migration and commuting patterns, it is found that shutting mobility in a few local places is favored against reducing mobility over the entire country network. In addition, commuting -and not migration-influences the spread level of the infection. The work offers an exclusive combined network-based and agent-based model that makes use of randomly generated mobility matrices.

Optimal control and stability analysis of an age-structured SEIRV model with imperfect vaccination.

Vaccination programs are crucial for reducing the prevalence of infectious diseases and ultimately eradicating them. A new age-structured SEIRV (S-Susceptible, E-Exposed, I-Infected, R-Recovered, V-Vaccinated) model with imperfect vaccination is proposed. After formulating our model, we show the existence and uniqueness of the solution using semigroup of operators. For stability analysis, we obtain a threshold parameter $ R_0 $. Through rigorous analysis, we show that if $ R_0 < 1 $, then the disease-free equilibrium point is stable. The optimal control strategy is also discussed, with the vaccination rate as the control variable. We derive the optimality conditions, and the form of the optimal control is obtained using the adjoint system and sensitivity equations. We also prove the uniqueness of the optimal controller. To visually illustrate our theoretical results, we also solve the model numerically.

Modelling the effect of non-pharmaceutical interventions on COVID-19 transmission from mobility maps.

The world has faced the COVID-19 pandemic for over two years now, and it is time to revisit the lessons learned from lockdown measures for theoretical and practical epidemiological improvements. The interlink between these measures and the resulting change in mobility (a predictor of the disease transmission contact rate) is uncertain. We thus propose a new method for assessing the efficacy of various non-pharmaceutical interventions (NPI) and examine the aptness of incorporating mobility data for epidemiological modelling. Facebook mobility maps for the United Arab Emirates are used as input datasets from the first infection in the country to mid-Oct 2020. Dataset was limited to the pre-vaccination period as this paper focuses on assessing the different NPIs at an early epidemic stage when no vaccines are available and NPIs are the only way to reduce the reproduction number ( R 0 ). We developed a travel network density parameter ß t to provide an estimate of NPI impact on mobility patterns. Given the infection-fatality ratio and time lag (onset-to-death), a Bayesian probabilistic model is adapted to calculate the change in epidemic development with ß t . Results showed that the change in ß t clearly impacted R 0 . The three lockdowns strongly affected the growth of transmission rate and collectively reduced R 0 by 78% before the restrictions were eased. The model forecasted daily infections and deaths by 2% and 3% fractional errors. It also projected what-if scenarios for different implementation protocols of each NPI. The developed model can be applied to identify the most efficient NPIs for confronting new COVID-19 waves and the spread of variants, as well as for future pandemics.

Evaluating COVID-19 control measures in mass gathering events with vaccine inequalities.

With the increasing global adoption of COVID-19 vaccines, limitations on mass gathering events have started to gradually loosen. However, the large vaccine inequality recorded among different countries is an important aspect that policymakers must address when implementing control measures for such events. In this paper, we propose a model for the assessment of different control measures with the consideration of vaccine inequality in the population. Two control measures are considered: selecting participants based on vaccine efficacy and restricting the event capacity. We build the model using agent-based modeling to capture the spatiotemporal crowd dynamics and utilize a genetic algorithm to assess the control strategies. This assessment is based on factors that are important for policymakers such as disease prevalence, vaccine diversity, and event capacity. A quantitative evaluation of vaccine diversity using the Simpson's Diversity Index is also provided. The Hajj ritual is used as a case study. We show that strategies that prioritized lowering the prevalence resulted in low event capacity but facilitated vaccine diversity. Moreover, strategies that prioritized diversity resulted in high infection rates. However, increasing the prioritization of participants with high vaccine efficacy significantly decreased the disease prevalence. Strategies that prioritized ritual capacity did not show clear trends.

Global dynamics of alcoholism epidemic model with distributed delays.

This paper aims to investigate the global dynamics of an alcoholism epidemic model with distributed delays. The main feature of this model is that it includes the effect of the social pressure as a factor of drinking. As a result, our global stability is obtained without a "basic reproduction number" nor threshold condition. Hence, we prove that the alcohol addiction will be always uniformly persistent in the population. This means that the investigated model has only one positive equilibrium, and it is globally asymptotically stable independent on the model parameters. This result is shown by proving that the unique equilibrium is locally stable, and the global attraction is shown using Lyapunov direct method.

On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems.

Given a discrete-time controlled bilinear systems with initial state x 0 and output function y i , we investigate the maximal output set Θ(Ω) = {x 0 ∈ ℝ n , y i ∈ Ω, ∀ i ≥ 0} where Ω is a given constraint set and is a subset of ℝ p . Using some stability hypothesis, we show that Θ(Ω) can be determined via a finite number of inequations. Also, we give an algorithmic process to generate the set Θ(Ω). To illustrate our theoretical approach, we present some examples and numerical simulations. Moreover, to demonstrate the effectiveness of our approach in real-life problems, we provide an application to the SI epidemic model and the SIR model.

Modeling the Impact of Unreported Cases of the COVID-19 in the North African Countries.

In this paper, we study a mathematical model investigating the impact of unreported cases of the COVID-19 in three North African countries: Algeria, Egypt, and Morocco. To understand how the population respects the restriction of population mobility implemented in each country, we use Google and Apple's mobility reports. These mobility reports help to quantify the effect of the population movement restrictions on the evolution of the active infection cases. We also approximate the number of the population infected unreported, the proportion of those that need hospitalization, and estimate the end of the epidemic wave. Moreover, we use our model to estimate the second wave of the COVID-19 Algeria and Morocco and to project the end of the second wave. Finally, we suggest some additional measures that can be considered to reduce the burden of the COVID-19 and would lead to a second wave of the spread of the virus in these countries.

Modeling the imported malaria to north Africa and the absorption effect of the immigrants.

As Malaria represents one of the major health burdens in Africa, there is a risk of reappearance of this vector-borne disease in malaria-free or low risk countries such as those in North Africa. One of the factors that can lead to this situation is the flow of sub-Saharan immigrants trying to reach Europe through North Africa. In this work, we investigate such a possibility via a mathematical model. We assume that the immigrant (non-locals) population has a carrying capacity that limits their numbers in the host country, and we study how they might contribute to the disease spread. Our analysis gave conditions of the persistence of the disease and showed that the non-local population could have a positive effect by reducing the spread of Malaria.

Cooperative system analysis of the Ebola virus epidemic model.

This paper aims to study the global stability of an Ebola virus epidemic model. Although this epidemic ended in September 2015, it devastated several West African countries and mobilized the international community. With the recent cases of Ebola in the Democratic Republic of the Congo (DRC), the threat of the reappearance of this fatal disease remains. Therefore, we are obligated to be prepared for a possible re-emerging of the disease. In this work, we investigate the global stability analysis via the theory of cooperative systems, and we determine the conditions that lead to global stability diseases free and endemic equilibrium.

Thalassemia in the United Arab Emirates: Why it can be prevented but not eradicated.

Thalassemia is a genetic blood disorder that causes abnormal hemoglobin. Hemoglobin is a protein in red blood cells that carries oxygen and is made of two proteins from four α-globin genes and two ß-globin genes. A defect in one or more of these genes causes thalassemia. The treatment of thalassemia mostly depends on life-long blood transfusions and removal of excessive iron from the blood stream. Such tremendous blood consumption puts pressure on the national blood stock in many countries. In particular, in the United Arab Emirates (UAE), various forms of thalassemia prevention have been used and hence, the substantial reduction of the thalassemia major population has been achieved. However, the thalassemia carrier population still remains high, which leads to the potential increase in the thalassemia major population through carrier-carrier marriages. In this work, we investigate the long-term impact and efficacy of thalassemia prevention measures via mathematical modeling at a population level. To our best knowledge, this type of assessment has not been done before and there is no mathematical model that has investigated such a problem for thalassemia or any blood disorders at a population level. By using UAE data, we perform numerical simulations of our model and conduct sensitivity analysis of parameter values to see which parameter values affect most the dynamics of our model. We discover that the prevention measures can contribute to reduce the prevalence of the disease only in the short term but not eradicate the disease in the long term.

Modeling the adaptive immune response in HBV infection.

The aim of this work is to investigate a new mathematical model that describes the interactions between Hepatitis B virus (HBV), liver cells (hepatocytes), and the adaptive immune response. The qualitative analysis of this as cytotoxic T lymphocytes (CTL) cells and the antibodies. These outcomes are (1) a disease free steady state, which its local stability is characterized as usual by R (0) < 1, (2) and the existence of four endemic steady states when R (0) > 1. The local stability of these steady states depends on functions of R (0). Our study shows that although we give conditions of stability of these steady states, not all conditions are feasible. This rules out the local stability of two steady states. The conditions of stability of the two other steady states (which represent the complete failure of the adaptive immunity and the persistence of the disease) are formulated based on the domination of CTL cells response or the antibody response.

Modeling the interaction of cytotoxic T lymphocytes and influenza virus infected epithelial cells.

The aim of this work is to investigate the mechanisms involved in the clearance of viral infection of the influenza virus at the epithelium level by modeling and analyzing the interaction of the influenza virus specific cytotoxic T Lymphocytes (CTL cells) and the influenza virus infected epithelial cells. Since detailed and definite mechanisms that trigger CTL production and cell death are still debatable, we utilize two plausible mathematical models for the CTLs response to influenza infection (i) logistic growth and (ii) threshold growth. These models incorporate the simulating effect of the production of CTLs during the infection. The systematical analysis of these models show that the behaviors of the models are similar when CTL density is high and in which case both generate reasonable dynamics. However, both models failed to produce the desirable and natural clearance dynamic. Nevertheless, at lower CTL density, the threshold model shows the possibility of existence of a "lower" equilibrium. This sub-threshold equilibrium may represent dose-dependent immune response to low level infection.

A viral load-based cellular automata approach to modeling HIV dynamics and drug treatment.

We formulated a novel cellular automata (CA) model for HIV dynamics and drug treatment. The model is built upon realistic biological processes, including the virus replication cycle and mechanisms of drug therapy. Viral load, its effect on infection rate, and the role of latently infected cells in sustaining HIV infection are among the aspects that are explored and incorporated in the model. We assume that the calculation of the number of cells in the neighborhood which influences the center cell's state is based on the viral load. This variable-cell neighborhood enables the simulation of an infection rate that is correlated to the viral load. This approach leads to a new and flexible way of modeling HIV dynamics and allows for the simulation of different antiretroviral drug treatments based on their individual and combined effects. The results of the simulation show the three phases of HIV dynamics (acute, chronic, and AIDS) and the additional drug response phase when drug treatment is added. The dynamics from the model qualitatively match clinical data. Drug treatment combinations with reverse transcriptase inhibitors and protease inhibitors are simulated using various drug efficacies. The results indicate that the model can be very useful in evaluating different drug therapy regimens.

An epidemic model with post-contact prophylaxis of distributed length I. Thresholds for disease persistence and extinction.

A possible control strategy against the spread of an infectious disease is the treatment with antimicrobials that are given prophylactically to those who had a contact with an infective person. The treatment continues until recovery or until it becomes obvious that there was no infection in the first place. The model considers susceptible, treated uninfected exposed, treated infected, (untreated) infectious, and recovered individuals. Since treatment lengths have an arbitrary distribution, the model system consists of ordinary differential and integral equations. A sharp threshold condition is established in terms of a basic replacement ratio (disease reproduction number) that separates disease extinction from uniform disease persistence. We use results from dynamical systems persistence theory proving the existence of a global compact attractor along the way. Existence and multiplicity of endemic equilibria are also studied.