A stochastic computing procedure to solve the dynamics of prevention in HIV system

An SVEIR SARS-CoV-2 Omicron variant model is proposed to provide some insights to coordinate non-pharmaceutical interventions (NPIs) and vaccination. Mathematically, we define the basic reproduction number R0 and the effective reproduction number Re to measure the infection potential of Omicron variant and formulate an optimal disease control strategy. Our inversion results imply that the sick period of Omicron variant in the United States is longer than that of Delta variant in India. The decrease in the infectious period of the infection with infectiousness implies that the risk of hospitalization is reduced; but the increasing period of the infection with non-infectiousness signifies that Omicron variant lengthens the period of nucleic acid test being negative. Optimistically, Omicron's death rate is only a quarter of Delta's. Moreover, we forecast that the cumulative cases will exceed 100 million in the United States on February 28, 2022, and the daily confirmed cases will reach a peak on February 2, 2022. The results of parameters sensitivity analysis imply that NPIs are helpful to reduce the number of confirmed cases. In particular, NPIs are indispensable even if all the people were vaccinated when the efficiency of vaccine is relatively low. By simulating the relationships of the effective reproduction number Re , the vaccination rate and the efficacy of vaccine, we find that it is impossible to achieve the herd immunity without NPIs while the efficiency of vaccine is lower than 88.7% . Therefore, the herd immunity area is defined by the evolution of relationships between the vaccination rate and the efficacy of vaccine. Finally, we present that the disease-induced mortality rate demonstrates the periodic oscillation and an almost periodic function is deduced to match the curve. A discussion completes the paper. 

/pdf/a-mathematical-model-reveals-the-influence-of-npis-and-3g3z827w.pdf

A mathematical model reveals the influence of NPIs and vaccination on SARS-CoV-2 Omicron Variant

The pandemic of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) took the world by surprise. Following the first outbreak of COVID-19 in December 2019, several models have been developed to study and understand its transmission dynamics. 
Although the spread of COVID-19 is being slowed down by vaccination and other interventions, there is still a need to have a clear understanding of the evolution of the pandemic across countries, states and communities.
To this end, there is a need to have a clearer picture of the initial spread of the disease in different regions.
In this project, we used a simple SEIR model and a Bayesian inference framework to estimate the basic reproduction number of COVID-19 across Africa. 
Our estimates vary between 1.98 (Sudan) and 9.66 (Mauritius), with a median of 3.67 (90% CrI: 3.31 - 4.12). The estimates provided in this paper will help to inform COVID-19 modeling in the respective countries/regions.

The basic reproduction number of COVID-19 across Africa

We developed an endemic model of COVID-19 to assess the impact of vaccination and immunity waning on the dynamics of the disease. Our model exhibits the phenomenon of backward bifurcation and bi-stability, where a stable disease-free equilibrium coexists with a stable endemic equilibrium. The epidemiological implication of this is that the control reproduction number being less than unity is no longer sufficient to guarantee disease eradication. We showed that this phenomenon could be eliminated by either increasing the vaccine efficacy or by reducing the disease transmission rate (adhering to non-pharmaceutical interventions). Furthermore, we numerically investigated the impacts of vaccination and waning of both vaccine-induced immunity and post-recovery immunity on the disease dynamics. Our simulation results show that the waning of vaccine-induced immunity has more effect on the disease dynamics relative to post-recovery immunity waning and suggests that more emphasis should be on reducing the waning of vaccine-induced immunity to eradicate COVID-19. 

/pdf/assessing-the-potential-impact-of-immunity-waning-on-the-3szlm0db.pdf

Assessing the potential impact of immunity waning on the dynamics of COVID-19 in South Africa: an endemic model of COVID-19

COVID-19 is a respiratory illness caused by an ribonucleic acid (RNA) virus prone to mutations. In December 2020, variants with different characteristics that could affect transmissibility emerged around the world. To address this new dynamic of the disease, we formulate and analyze a mathematical model of a two-strain COVID-19 transmission dynamics with strain 1 vaccination. The model is theoretically analyzed and sufficient conditions for the stability of its equilibria are derived. In addition to the disease-free and endemic equilibria, the model also has single-strain 1 and strain 2 endemic equilibria. Using the center manifold theory, it is shown that the model does not exhibit the phenomenon of backward bifurcation, and global stability of the model equilibria are proved using various approaches. Simulations to support the model theoretical results are provided. We calculate the basic reproductive number R1 and R2 for both strains independently. Results indicate that – both strains will persist when R1>1 and R2>1 – Stain 2 could establish itself as the dominant strain if R1<1 and R2>1, or when R2>R1>1. However, because of de novo herd immunity due to strain 1 vaccine efficacy and provided the initial stain 2 transmission threshold parameter R2 is controlled to remain below unity, strain 2 will not establish itself/persist in the community. 

Dynamic of a two-strain COVID-19 model with vaccination

In this paper, we develop a new disease-resistant mathematical model with a fraction of the susceptible class under imperfect vaccine and treatment of both the symptomatic and quarantine classes. With standard incidence when the associated reproduction threshold is less than unity, the model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium. It is then proved that this phenomenon vanishes either when the vaccine is assumed to be 100% potent and perfect or the Standard Incidence is replaced with a Mass Action Incidence in the model development. Furthermore, the model has a unique endemic and disease-free equilibria. Using a suitable Lyapunov function, the endemic equilibrium and disease free equilibrium are proved to be globally-asymptotically stable depending on whether the control reproduction number is less or greater than unity. Some numerical simulations are presented to validate the analytic results.

/pdf/mathematical-analysis-of-a-disease-resistant-model-with-3a9omuj7th.pdf

Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment

Adherence to public health policies such as the non-pharmaceutical interventions implemented against COVID-19 plays a major role in reducing infections and controlling the spread of the diseases. In addition, understanding the transmission dynamics of the disease is also important in order to make and implement efficient public health policies. In this paper, we developed an SEIR-type compartmental model to assess the impact of adherence to COVID-19 non-pharmaceutical interventions and indirect transmission on the dynamics of the disease. Our model considers both direct and indirect transmission routes and stratifies the population into two groups: those that adhere to COVID-19 non-pharmaceutical interventions (NPIs) and those that do not adhere to the NPIs. We compute the control reproduction number and the final epidemic size relation for our model and study the effect of different parameters of the model on these quantities. Our results show that direct transmission has more effect on the reproduction number and final epidemic size, relative to indirect transmission. In addition, we showed that there is a significant benefit in adhering to the COVID-19 NPIs.

/pdf/assessing-the-impact-of-adherence-to-non-pharmaceutical-28731t6cwx.pdf

Assessing the impact of adherence to Non-pharmaceutical interventions and indirect transmission on the dynamics of COVID-19: a mathematical modelling study

Adherence to public health policies such as the non-pharmaceutical interventions implemented against COVID-19 plays a major role in reducing infections and controlling the spread of the diseases. In addition, understanding the transmission dynamics of the disease is also important in order to make and implement efficient public health policies. In this paper, we developed an SEIR-type compartmental model to assess the impact of adherence to COVID-19 non-pharmaceutical interventions and indirect transmission on the dynamics of the disease. Our model considers both direct and indirect transmission routes and stratifies the population into two groups: those that adhere to COVID-19 non-pharmaceutical interventions (NPIs) and those that do not adhere to the NPIs. We compute the control reproduction number and the final epidemic size relation for our model and study the effect of different parameters of the model on these quantities. Our results show that there is a significant benefit in adhering to the COVID-19 NPIs.

Assessing the impact of adherence to Non-pharmaceutical interventions and indirect transmission on the dynamics of COVID-19: a mathematical modelling study.

We develop a virus-resistant HIV-1 mathematical model with behavioural change in HIV-1 resistant non-progressors. The model has both disease-free and endemic equilibrium points that are proved to be locally asymptotically stable depending on the value of the associated reproduction numbers. In both models, a non-linear Goh{Volterra Lyapunov function was used to prove that the endemic equilibrium point is globally asymptotically stable for special case while the method of Castillo-Chavez was used to prove the global asymptotic stability of the disease-free equilibrium point. In both the analytic and numerical results, this study shows that in the context of resistance to HIV/AIDS, total abstinence can also play an important role in protection against this notorious infectious disease.

/pdf/analysis-of-a-virus-resistant-hiv-1-model-with-behavior-4ldyx1duvx.pdf

Musa Rabiu

Papers

Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment

The basic reproduction number of COVID-19 across Africa

Assessing the impact of adherence to Non-pharmaceutical interventions and indirect transmission on the dynamics of COVID-19: a mathematical modelling study

Assessing the impact of adherence to Non-pharmaceutical interventions and indirect transmission on the dynamics of COVID-19: a mathematical modelling study.

Analysis of a virus-resistant HIV-1 model with behavior change in non-progressors