During decades, mathematical models have been used to predict the behavior of physical and biologic systems, and to define strategies aiming the minimization of the effects regarding different types of diseases. In the present days, the development of mathematical models to simulate the dynamic behavior of novel coronavirus disease (COVID-19) is considered an important theme due to the quantity of infected people worldwide. In this work, the aim is to determine an optimal control strategy for vaccine administration in COVID-19 pandemic treatment considering real data from China. For this purpose, an inverse problem is formulated and solved in order to determine the parameters of the compartmental SIR (Susceptible-Infectious-Recovered) model. To solve such inverse problem, the Differential Evolution (DE) algorithm is employed. After this step, two optimal control problems (mono- and multi-objective) to determine the optimal strategy for vaccine administration in COVID-19 pandemic treatment are proposed. The first consists of minimizing the quantity of infected individuals during the treatment. The second considers minimizing together the quantity of infected individuals and the prescribed vaccine concentration during the treatment, i.e., a multi-objective optimal control problem. The solution of each optimal control problems is obtained using DE and Multi-Objective Differential Evolution (MODE) algorithms, respectively. The results regarding the proposed multi-objective optimal control problem provides a set of evidences from which an optimal strategy for vaccine administration can be chosen, according to a given criterion.
How to strategically allocate the available vaccines is a crucial issue for pandemic control. In this work, we propose a mathematical framework for optimal stabilizing vaccine allocation, where our goal is to send the infections to zero as soon as possible with a fixed number of vaccine doses. This framework allows us to efficiently compute the optimal vaccine allocation policy for general epidemic spread models including SIS/SIR/SEIR and a new model of COVID-19 transmissions. By fitting the real data in New York State to our framework, we found that the optimal stabilizing vaccine allocation …
With the invention of the COVID-19 vaccine, shipping and distributing are crucial in controlling the pandemic. In this paper, we build a mean-field variational problem in a spatial domain, which controls the propagation of pandemic by the optimal transportation strategy of vaccine distribution. Here we integrate the vaccine distribution into the mean-field SIR model designed in our previous paper arXiv:2006.01249. Numerical examples demonstrate that the proposed model provides practical strategies in vaccine distribution on a spatial domain.
Besides maintaining health precautions, vaccination has been the only prevention from SARS-CoV-2, though no clinically proved 100% effective vaccine has been developed till date. At this stage, to withhold the debris of this pandemic, experts need to know the impact of the vaccine efficacy rate's threshold and how long this pandemic may extent with vaccines that have different efficacy rates. In this article, a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing pandemic. We simulated a five compartment mathematical model to ana…
In this paper we find common features between the equations that are used for pandemic or epidemic modeling and the renormalization group equations that are used in high energy physics. Some of these features include the relation of contact matrices in pandemic modeling and operator mixing in the renormalization group equations. Another common feature are the use of flow diagrams and the study of fixed points both in pandemic modeling and in evolution under renormalization group equations. We illustrate these relations through the study of some cases of interest to the current COVID-19 pandemi…
The development and authorization of COVID-19 vaccines has provided the clearest path forward to eliminate community spread hence end the ongoing SARS-CoV-2 pandemic. However, the limited pace at which the vaccine can be administered motivates the question, to what extent must we continue to adhere to social intervention measures such as mask wearing and social distancing? To address this question, we develop a mathematical model of COVID-19 spread incorporating both vaccine dynamics and socio-epidemiological parameters. We use this model to study two important measures of disease control and …
The Severe Acute Respiratory Syndrome Corona Virus 2 (SARS-CoV-2), or Covid-19, burst into a pandemic in the beginning of 2020. An unprecedented worldwide effort involving academic institutions, regulatory agencies and industry is facing the challenges imposed by the rapidly spreading disease. Emergency use authorization for vaccines were granted in the beginning of December 2020 in Europe and nine days later in the United States. The urge for vaccination started a race, forcing governs and health care agencies to take decisions on the fly regarding the vaccination strategy and logistics. So f…
During the Covid-19 pandemic a key role is played by vaccination to combat the virus. There are many possible policies for prioritizing vaccines, and different criteria for optimization: minimize death, time to herd immunity, functioning of the health system. Using an age-structured population compartmental finite-dimensional optimal control model, our results suggest that the eldest to youngest vaccination policy is optimal to minimize deaths. Our model includes the possible infection of vaccinated populations. We apply our model to real-life data from the US Census for New Jersey and Florida…
Since early 2020, the world has been dealing with a raging pandemic outbreak: COVID-19. A year later, vaccines have become accessible, but in limited quantities, so that governments needed to devise a strategy to decide which part of the population to prioritize when assigning the available doses, and how to manage the interval between doses for multi-dose vaccines. In this paper, we present an optimization framework to address the dynamic double-dose vaccine allocation problem whereby the available vaccine doses must be administered to different age-groups to minimize specific societal object…
The COVID-19 pandemic has severely impacted health systems and economies worldwide. Significant global efforts are therefore ongoing to improve vaccine efficacies, optimize vaccine deployment, and develop new antiviral therapies to combat the pandemic. Mechanistic viral dynamics and quantitative systems pharmacology models of SARS-CoV-2 infection, vaccines, immunomodulatory agents, and antiviral therapeutics have played a key role in advancing our understanding of SARS-CoV-2 pathogenesis and transmission, the interplay between innate and adaptive immunity to influence the outcomes of infection…
In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory can be a useful tool based on solid mathematical bases to plan the vaccination campaign in the direction of eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitali…
The outbreak of COVID-19 led to a record-breaking race to develop a vaccine. However, the limited vaccine capacity creates another massive challenge: how to distribute vaccines to mitigate the near-end impact of the pandemic? In the United States in particular, the new Biden administration is launching mass vaccination sites across the country, raising the obvious question of where to locate these clinics to maximize the effectiveness of the vaccination campaign. This paper tackles this question with a novel data-driven approach to optimize COVID-19 vaccine distribution. We first augment a sta…
Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health. In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic. We start revisiting the basic properties of simple Kermack-McKendrick type models. Then, we discuss extensions of such models and important epidemiological quantities applied to investigate the role of heterogeneity in disease transmission e.g. mixing functions and superspreading events, …
Stanford University（斯坦福大学）；National University of Singapore（新加坡国立大学）；Imperial College London（帝国理工学院）
Since COVID-19 vaccines became available, no studies have quantified how different disaster evacuation strategies can mitigate pandemic risks in shelters. Therefore, we applied an age-structured epidemiological model, known as the Susceptible-Exposed-Infectious-Recovered (SEIR) model, to investigate to what extent different vaccine uptake levels and the Diversion protocol implemented in Taiwan decrease infections and delay pandemic peak occurrences. Taiwan's Diversion protocol involves diverting those in self-quarantine due to exposure, thus preventing them from mingling with the general publi…
Non-pharmaceutical interventions(NPIs) play an important role in the early stage control of COVID-19 pandemic. Vaccination is considered to be the inevitable course to stop the spread of SARS-CoV-2. Based on the mechanism, a SVEIR COVID-19 model with vaccination and NPIs is proposed. By means of the basic reproduction number $R_{0}$, it is shown that the disease-free equilibrium is globally attractive if $\mathscr{R}_{0}<1$, and COVID-19 is uniform persistence if $\mathscr{R}_{0}>1$. Taking Indian dates for example in the numerical simulation, we find that our dynamical results fits well with …
The COVID-19 pandemic has influenced the lives of people globally. In the past year many researchers have proposed different models and approaches to explore in what ways the spread of the disease could be mitigated. One of the models that have been used a great deal is the Susceptible-Exposed-Infectious-Recovered (SEIR) model. Some researchers have modified the traditional SEIR model, and proposed new versions of it. However, to the best of our knowledge, the state-of-the-art papers have not considered the effect of different vaccine types, meaning single shot and double shot vaccines, in the…
Since the end of 2019, COVID-19 has significantly affected the lives of people around the world. Towards the end of 2020, several COVID-19 vaccine candidates with relatively high efficacy have been reported in the final phase of clinical trials. Vaccines have been considered as critical tools for opening up social and economic activities, thereby lessening the impact of this disease on the society. This paper presents a simulation of COVID-19 spread using modified Susceptible-Infected-Removed (SIR) model under vaccine intervention in several localities of Malaysia, i.e. those cities or states …
Since the recent introduction of several viable vaccines for SARS-CoV-2, vaccination uptake has become the key factor that will determine our success in containing the COVID-19 pandemic. We argue that game theory and social network models should be used to guide decisions pertaining to vaccination programmes for the best possible results. In the months following the introduction of vaccines, their availability and the human resources needed to run the vaccination programmes have been scarce in many countries. Vaccine hesitancy is also being encountered from some sections of the general public.…
In more than two years since the COVID-19 virus was first detected in China, hundreds of millions of individuals have been infected, and millions have died. Aside from the immediate need for medical solutions (such as vaccines and medications) to treat the epidemic, the Corona pandemic has strengthened the demand for mathematical models that can predict the spread of the pandemic in an ever-changing reality. Here, we present a novel, dynamic particle model based on the basic principles of statistical physics that enables the prediction of the spreading of Covid-19 in the presence of effective …
Since December 2020, variants of COVID-19 (especially Delta and Omicron) appeared with different characteristics that influenced death and transmissibility emerged around the world. To address the novel dynamics of the disease, we propose a dynamical model of two strains, namely native and mutant, transmission dynamics with mutation and imperfect vaccination. It is also assumed that the recuperated individuals from the native strain can be infected with mutant strain through the direct contact with individual or contaminated surfaces or aerosols. We compute the basic reproduction number for ea…
SARS-CoV-2 is a severe respiratory infection that infects humans. Its outburst entitled it as a pandemic emergence. To get a grip on this, outbreak specific preventive and therapeutic interventions are urgently needed. It must be said that, until now, there are no existing vaccines for coronaviruses. To promptly and rapidly respond to pandemic events, the application of in silico trials can be used for designing and testing medicines against SARS-CoV-2 and speed-up the vaccine discovery pipeline, predicting any therapeutic failure and minimizing undesired effects. Here, we present an in silico…
Population-wide vaccination is critical for containing the SARS-CoV-2 (Covid-19) pandemic when combined with restrictive and prevention measures. In this study, we introduce SAIVR, a mathematical model able to forecast the Covid-19 epidemic evolution during the vaccination campaign. SAIVR extends the widely used Susceptible-Infectious-Removed (SIR) model by considering the Asymptomatic (A) and Vaccinated (V) compartments. The model contains several parameters and initial conditions that are estimated by employing a semi-supervised machine learning procedure. After training an unsupervised neur…
By the end of 2020, a year since the first cases of infection by the Covid-19 virus have been reported, there is a light at the end of the tunnel. Several pharmaceutical companies made significant progress in developing effective vaccines against the Covid-19 virus that has claimed the lives of more than a million people over the world. On the other hand, there is growing evidence of re-infection by the virus, which can cause further outbreaks. In this paper, we apply statistical physics tools to examine the vaccination rate required to control the pandemic for three different vaccine efficien…
The potential waning of the vaccination immunity to COVID-19 could pose threats to public health, as it is tenable that the timing of such waning would synchronize with the near-complete restoration of normalcy. Should also testing be relaxed, we might witness a resurgent COVID-19 wave in winter 2021/2022. In response to this risk, an additional vaccine dose, the booster shot, is being administered worldwide. In a projected study with an outlook of six months, we explore the interplay between the rate at which boosters are distributed and the extent to which testing practices are implemented, …
COVID-19 will be a continuous threat to human population despite having a few vaccines at hand until we reach the endemic state through natural herd immunity and total immunization through universal vaccination. However, the vaccine acts as a practical tool for reducing the massive public health problem and the emerging economic consequences that the continuing COVID -19 epidemic is causing worldwide, while the vaccine efficacy wanes. In this work, we propose and analyze an epidemic model of Susceptible-Exposed-Infected-Recovered-Vaccinated (SEIRV) population taking into account the rate of va…
Non-pharmaceutical interventions have been critical in the fight against the COVID-19 pandemic. However, these sanitary measures have been partially lifted due to socioeconomic factors causing a worrisome rebound of the epidemic in several countries. In this work, we assess the effectiveness of the mitigation implemented to constrain the spread of SARS-CoV-2 in the Mexican territory during 2020. We also investigate to what extent the initial deployment of the vaccine will help to mitigate the pandemic and reduce the need for social distancing and other mobility restrictions. Our modeling appro…
COVID-19 has devastated the entire global community. Vaccines present an opportunity to mitigate the pandemic; however, the effect of vaccination coupled with the behavioral response of the population is not well understood. We propose a model that incorporates two important dynamically varying population behaviors: level of caution and sense of safety. Level of caution increases with the number of infectious cases, while an increasing sense of safety with increased vaccination lowers precautionary behaviors. To the best of our knowledge, this is the first model that can effectively reproduce …
The unfolding of pandemic influenza A(H1N1) for Fall 2009 in the Northern Hemisphere is still uncertain. Plans for vaccination campaigns and vaccine trials are underway, with the first batches expected to be available early October. Several studies point to the possibility of an anticipated pandemic peak that could undermine the effectiveness of vaccination strategies. Here we use a structured global epidemic and mobility metapopulation model to assess the effectiveness of massive vaccination campaigns for the Fall/Winter 2009. Mitigation effects are explored depending on the interplay between…
We studied the COVID-19 pandemic evolution in selected African countries. For each country considered, we modeled simultaneously the data of the active, recovered and death cases. In this study, we used a year of data since the first cases were reported. We estimated the time-dependent basic reproduction numbers, $R_0$, and the fractions of infected but unaffected populations, to offer insights into containment and vaccine strategies in African countries. We found that $R_0\leq 4$ at the start of the pandemic but has since fallen to $R_0 \sim 1$. The unaffected fractions of the populations stu…
In the absence of any available vaccines or drugs, prevention of the spread of Coronavirus Disease 2019 (COVID-19) pandemic is being achieved by putting many mitigation measures in place. It is indispensable to have robust and reliable ways of evaluating the effectiveness of these measures. In this work, we assume that, at a very coarse-grained level of description, the overall effect of all the mitigation measures is that we can still describe the spread of the pandemic using the most basic Susceptible-Exposed-Infectious-Removed ($SEIR$) model but with an "effective contact rate" ($β$) which …
The rapid development of vaccines to combat the spread of COVID-19 disease caused by the SARS-CoV-2 virus is a great scientific achievement. Before the development of the COVID-19 vaccines, most studies capitalized on the available data that did not include pharmaceutical measures. Such studies focused on the impact of non-pharmaceutical measures (e.g social distancing, sanitation, wearing of face masks, and lockdown) to study the spread of COVID-19. In this study, we used the SIDARTHE-V model which is an extension of the SIDARTHE model wherein we include vaccination roll outs. We studied the …
This study aims to determine an optimal control strategy for vaccine scheduling in COVID-19 pandemic treatment by converting widely acknowledged infectious disease model named SEIR into an optimal control problem. The problem is augmented by adding medication and vaccine limitations to match real-world situations. Two version of the problem is formulated to minimize the number of infected individuals at the same provide the optimal vaccine possible to reduce the susceptible population to a considerably lower state. Optimal control problems are solved using RBF-Galerkin method. These problems a…
As 2021 dawns, the COVID-19 pandemic is still raging strongly as vaccines finally appear and hopes for a return to normalcy start to materialize. There is much to be learned from the pandemic's first year data that will likely remain applicable to future epidemics and possible pandemics. With only minor variants in virus strain, countries across the globe have suffered roughly the same pandemic by first glance, yet few locations exhibit the same patterns of viral spread, growth, and control as the state of Hawai'i. In this paper, we examine the data and compare the COVID-19 spread statistics b…
Traditional vaccines against viruses are designed to target their surface proteins, i.e., antigens, which can trigger the immune system to produce specific antibodies to capture and neutralize the viruses. However, viruses often evolve quickly, and their antigens are prone to mutations to avoid recognition by the antibodies (antigenic drift). This limitation of the antibody-mediated immunity could be addressed by the T-cell mediated immunity, which is able to recognize conserved viral HLA peptides presented on virus-infected cells. Thus, by targeting conserved regions on the genome of a virus,…
With the present highly infectious dominant SARS-CoV-2 strain of B1.1.529 or Omicron spreading around the globe, there is concern that the COVID-19 pandemic will not end soon and that it will be a race against time until a more contagious and virulent variant emerges. One of the most promising approaches for preventing virus propagation is to maintain continuous high vaccination efficacy among the population, thereby strengthening the population protective effect and preventing the majority of infection in the vaccinated population, as is known to occur with the Omicron variant frequently. Cou…
The COVID-19 pandemic has placed unprecedented demands on local public health units in Ontario, Canada, one of which was the need for in-house epidemiological-modelling capabilities. To address this need, Ontario Tech University and the Durham Region Health Department developed a native Windows desktop app that performs epidemiological modelling of infectious diseases. The app is an implementation of a multi-stratified compartmental epidemiological model that can accommodate multiple virus variants and levels of vaccination, as well as public health measures such as physical distancing, contac…
A pandemic, the worldwide spread of a disease, can threaten human beings from the social as well as biological perspectives and paralyze existing living habits. To stave off the more devastating disaster and return to a normal life, people make tremendous efforts at multiscale levels from individual to worldwide: paying attention to hand hygiene, developing social policies such as wearing masks, social distancing, quarantine, and inventing vaccines and remedy. Regarding the current severe pandemic, namely the coronavirus disease 2019, we explore the spreading-suppression effect when adopting t…
