Effect of stochasticity on coinfection dynamics of respiratory viruses.

BACKGROUND: Respiratory viral infections are a leading cause of mortality worldwide. As many as 40% of patients hospitalized with influenza-like illness are reported to be infected with more than one type of virus. However, it is not clear whether these infections are more severe than single viral infections. Mathematical models can be used to help us understand the dynamics of respiratory viral coinfections and their impact on the severity of the illness. Most models of viral infections use ordinary differential equations (ODE) that reproduce the average behavior of the infection, however, they might be inaccurate in predicting certain events because of the stochastic nature of viral replication cycle. Stochastic simulations of single virus infections have shown that there is an extinction probability that depends on the size of the initial viral inoculum and parameters that describe virus-cell interactions. Thus the coinfection dynamics predicted by the ODE might be difficult to observe in reality. RESULTS: In this work, a continuous-time Markov chain (CTMC) model is formulated to investigate probabilistic outcomes of coinfections. This CTMC model is based on our previous coinfection model, expressed in terms of a system of ordinary differential equations. Using the Gillespie method for stochastic simulation, we examine whether stochastic effects early in the infection can alter which virus dominates the infection. CONCLUSIONS: We derive extinction probabilities for each virus individually as well as for the infection as a whole. We find that unlike the prediction of the ODE model, for similar initial growth rates stochasticity allows for a slower growing virus to out-compete a faster growing virus.

Superinfection and cell regeneration can lead to chronic viral coinfections.

Molecular diagnostic techniques have revealed that approximately 43% of the patients hospitalized with influenza-like illness are infected by more than one viral pathogen, sometimes leading to long-lasting infections. It is not clear how the heterologous viruses interact within the respiratory tract of the infected host to lengthen the duration of what are usually short, self-limiting infections. We develop a mathematical model which allows for single cells to be infected simultaneously with two different respiratory viruses (superinfection) to investigate the possibility of chronic coinfections. We find that a model with superinfection and cell regeneration has a stable chronic coinfection fixed point, while superinfection without cell regeneration produces only acute infections. This analysis suggests that both superinfection and cell regeneration are required to sustain chronic coinfection via this mechanism since coinfection is maintained by superinfected cells that allow slow-growing infections a chance to infect cells and continue replicating. This model provides a possible mechanism for chronic coinfection independent of any viral interactions via the immune response.

The rate of viral transfer between upper and lower respiratory tracts determines RSV illness duration.

Respiratory syncytial virus can lead to serious lower respiratory infection (LRI), particularly in children and the elderly. LRI can cause longer infections, lingering respiratory problems, and higher incidence of hospitalization. In this paper, we use a simplified ordinary differential equation model of viral dynamics to study the role of transport mechanisms in the occurrence of LRI. Our model uses two compartments to simulate the upper respiratory tract and the lower respiratory tract (LRT) and assumes two distinct types of viral transfer between the two compartments: diffusion and advection. We find that a range of diffusion and advection values lead to long-lasting infections in the LRT, elucidating a possible mechanism for the severe LRI infections observed in humans.

Modeling of fusion inhibitor treatment of RSV in African green monkeys.

Respiratory syncytial virus (RSV) is a respiratory infection that can cause serious illness, particularly in infants. In this study, we test four different model implementations for the effect of a fusion inhibitor, including one model that combines different drug effects, by fitting the models to data from a study of TMC353121 in African green monkeys. We use mathematical modeling to estimate the drug efficacy parameters, εmax, the maximum efficacy of the drug, and EC50, the drug concentration needed to achieve half the maximum effect. We find that if TMC353121 is having multiple effects on viral kinetics, more detailed data, using different treatment delays, is needed to detect this effect.

Learning from the COVID-19 pandemic: a systematic review of mathematical vaccine prioritization models.

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.

Mathematical modeling for estimating influenza vaccine efficacy: A case study of the Valencian Community, Spain.

Vaccine efficacy and its quantification is a crucial concept for the proper design of public health vaccination policies. In this work we proposed a mathematical model to estimate the efficacy of the influenza vaccine in a real-word scenario. In particular, our model is a SEIR-type epidemiological model, which distinguishes vaccinated and unvaccinated populations. Mathematically, its dynamics is governed by a nonlinear system of ordinary differential equations, where the non-linearity arises from the effective contacts between susceptible and infected individuals. Two key aspects of this study is that we use a vaccine distribution over time that is based on real data specific to the elderly people in the Valencian Community and the calibration process takes into account that over one influenza season a specific proportion of the population becomes infected with influenza. To consider the effectiveness of the vaccine, the model incorporates a parameter, the vaccine attenuation factor, which is related with the vaccine efficacy against the influenza virus. With this framework, in order to calibrate the model parameters and to obtain an influenza vaccine efficacy estimation, we considered the 2016-2017 influenza season in the Valencian Community, Spain, using the influenza reported cases of vaccinated and unvaccinated. In order to ensure the model identifiability, we choose to deterministically calibrate the parameters for different scenarios and we find the one with the minimum error in order to determine the vaccine efficacy. The calibration results suggest that the influenza vaccine developed for 2016-2017 influenza season has an efficacy of approximately 76.7%, and that the risk of becoming infected is five times higher for an unvaccinated individual in comparison with a vaccinated one. This estimation partially agrees with some previous studies related to the influenza vaccine. This study presents a new integrated mathematical approach to study the influenza vaccine efficacy and gives further insight into this important public health topic.

Mathematical Modeling of SARS-CoV-2 Omicron Wave under Vaccination Effects.

Over the course of the COVID-19 pandemic millions of deaths and hospitalizations have been reported. Different SARS-CoV-2 variants of concern have been recognized during this pandemic and some of these variants of concern have caused uncertainty and changes in the dynamics. The Omicron variant has caused a large amount of infected cases in the US and worldwide. The average number of deaths during the Omicron wave toll increased in comparison with previous SARS-CoV-2 waves. We studied the Omicron wave by using a highly nonlinear mathematical model for the COVID-19 pandemic. The novel model includes individuals who are vaccinated and asymptomatic, which influences the dynamics of SARS-CoV-2. Moreover, the model considers the waning of the immunity and efficacy of the vaccine against the Omicron strain. This study uses the facts that the Omicron strain has a higher transmissibility than the previous circulating SARS-CoV-2 strain but is less deadly. Preliminary studies have found that Omicron has a lower case fatality rate compared to previous circulating SARS-CoV-2 strains. The simulation results show that even if the Omicron strain is less deadly it might cause more deaths, hospitalizations and infections. We provide a variety of scenarios that help to obtain insight about the Omicron wave and its consequences. The proposed mathematical model, in conjunction with the simulations, provides an explanation for a large Omicron wave under various conditions related to vaccines and transmissibility. These results provide an awareness that new SARS-CoV-2 variants can cause more deaths even if their fatality rate is lower.

Study of optimal vaccination strategies for early COVID-19 pandemic using an age-structured mathematical model: A case study of the USA.

In this paper we study different vaccination strategies that could have been implemented for the early COVID-19 pandemic. We use a demographic epidemiological mathematical model based on differential equations in order to investigate the efficacy of a variety of vaccination strategies under limited vaccine supply. We use the number of deaths as the metric to measure the efficacy of each of these strategies. Finding the optimal strategy for the vaccination programs is a complex problem due to the large number of variables that affect the outcomes. The constructed mathematical model takes into account demographic risk factors such as age, comorbidity status and social contacts of the population. We perform simulations to assess the performance of more than three million vaccination strategies which vary depending on the vaccine priority of each group. This study focuses on the scenario corresponding to the early vaccination period in the USA, but can be extended to other countries. The results of this study show the importance of designing an optimal vaccination strategy in order to save human lives. The problem is extremely complex due to the large amount of factors, high dimensionality and nonlinearities. We found that for low/moderate transmission rates the optimal strategy prioritizes high transmission groups, but for high transmission rates, the optimal strategy focuses on groups with high CFRs. The results provide valuable information for the design of optimal vaccination programs. Moreover, the results help to design scientific vaccination guidelines for future pandemics.

Mathematical modeling to study the impact of immigration on the dynamics of the COVID-19 pandemic: A case study for Venezuela.

We propose two different mathematical models to study the effect of immigration on the COVID-19 pandemic. The first model does not consider immigration, whereas the second one does. Both mathematical models consider five different subpopulations: susceptible, exposed, infected, asymptomatic carriers, and recovered. We find the basic reproduction number R0 using the next-generation matrix method for the mathematical model without immigration. This threshold parameter is paramount because it allows us to characterize the evolution of the disease and identify what parameters substantially affect the COVID-19 pandemic outcome. We focus on the Venezuelan scenario, where immigration and emigration have been important over recent years, particularly during the pandemic. We show that the estimation of the transmission rates of the SARS-CoV-2 are affected when the immigration of infected people is considered. This has an important consequence from a public health perspective because if the basic reproduction number is less than unity, we can expect that the SARS-CoV-2 would disappear. Thus, if the basic reproduction number is slightly above one, we can predict that some mild non-pharmaceutical interventions would be enough to decrease the number of infected people. The results show that the dynamics of the spread of SARS-CoV-2 through the population must consider immigration to obtain better insight into the outcomes and create awareness in the population regarding the population flow.

Dynamics of toxoplasmosis in the cat's population with an exposed stage and a time delay.

We propose a new mathematical model to investigate the effect of the introduction of an exposed stage for the cats who become infected with the T. gondii parasite, but that are not still able to produce oocysts in the environment. The model considers a time delay in order to represent the duration of the exposed stage. Besides the cat population the model also includes the oocysts related to the T. gondii in the environment. The model includes the cats since they are the only definitive host and the oocysts, since they are relevant to the dynamics of toxoplasmosis. The model considers lifelong immunity for the recovered cats and vaccinated cats. In addition, the model considers that cats can get infected through an effective contact with the oocysts in the environment. We find conditions such that the toxoplasmosis disease becomes extinct. We analyze the consequences of considering the exposed stage and the time delay on the stability of the equilibrium points. We numerically solve the constructed model and corroborated the theoretical results.

Impact of Infective Immigrants on COVID-19 Dynamics.

The COVID-19 epidemic is an unprecedented and major social and economic challenge worldwide due to the various restrictions. Inflow of infective immigrants have not been given prominence in several mathematical and epidemiological models. To investigate the impact of imported infection on the number of deaths, cumulative infected and cumulative asymptomatic, we formulate a mathematical model with infective immigrants and considering vaccination. The basic reproduction number of the special case of the model without immigration of infective people is derived. We varied two key factors that affect the transmission of COVID-19, namely the immigration and vaccination rates. In addition, we considered two different SARS-CoV-2 transmissibilities in order to account for new more contagious variants such as Omicron. Numerical simulations using initial conditions approximating the situation in the US when the vaccination program was starting show that increasing the vaccination rate significantly improves the outcomes regarding the number of deaths, cumulative infected and cumulative asymptomatic. Other factors are the natural recovery rates of infected and asymptomatic individuals, the waning rate of the vaccine and the vaccination rate. When the immigration rate is increased significantly, the number of deaths, cumulative infected and cumulative asymptomatic increase. Consequently, accounting for the level of inflow of infective immigrants may help health policy/decision-makers to formulate policies for public health prevention programs, especially with respect to the implementation of the stringent preventive lock down measure.

Model Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility.

During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models. This document summarizes these discussions, presents difficulties, and mentions existing efforts towards future solutions that will allow future model utility and integration. We argue that without addressing these challenges, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises we face.

Analysis of Delayed Vaccination Regimens: A Mathematical Modeling Approach.

The first round of vaccination against coronavirus disease 2019 (COVID-19) began in early December of 2020 in a few countries. There are several vaccines, and each has a different efficacy and mechanism of action. Several countries, for example, the United Kingdom and the USA, have been able to develop consistent vaccination programs where a great percentage of the population has been vaccinated (May 2021). However, in other countries, a low percentage of the population has been vaccinated due to constraints related to vaccine supply and distribution capacity. Countries such as the USA and the UK have implemented different vaccination strategies, and some scholars have been debating the optimal strategy for vaccine campaigns. This problem is complex due to the great number of variables that affect the relevant outcomes. In this article, we study the impact of different vaccination regimens on main health outcomes such as deaths, hospitalizations, and the number of infected. We develop a mathematical model of COVID-19 transmission to focus on this important health policy issue. Thus, we are able to identify the optimal strategy regarding vaccination campaigns. We find that for vaccines with high efficacy (>70%) after the first dose, the optimal strategy is to delay inoculation with the second dose. On the other hand, for a low first dose vaccine efficacy, it is better to use the standard vaccination regimen of 4 weeks between doses. Thus, under the delayed second dose option, a campaign focus on generating a certain immunity in as great a number of people as fast as possible is preferable to having an almost perfect immunity in fewer people first. Therefore, based on these results, we suggest that the UK implemented a better vaccination campaign than that in the USA with regard to time between doses. The results presented here provide scientific guidelines for other countries where vaccination campaigns are just starting, or the percentage of vaccinated people is small.

Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness.

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number 𝓡 0 using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population.

Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach.

The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020. Currently, there are only a few approved vaccines, each with different efficacies and mechanisms of action. Moreover, vaccination programs in different regions may vary due to differences in implementation, for instance, simply the availability of the vaccine. In this article, we study the impact of the pace of vaccination and the intrinsic efficacy of the vaccine on prevalence, hospitalizations, and deaths related to the SARS-CoV-2 virus. Then we study different potential scenarios regarding the burden of the COVID-19 pandemic in the near future. We construct a compartmental mathematical model and use computational methodologies to study these different scenarios. Thus, we are able to identify some key factors to reach the aims of the vaccination programs. We use some metrics related to the outcomes of the COVID-19 pandemic in order to assess the impact of the efficacy of the vaccine and the pace of the vaccine inoculation. We found that both factors have a high impact on the outcomes. However, the rate of vaccine administration has a higher impact in reducing the burden of the COVID-19 pandemic. This result shows that health institutions need to focus on increasing the vaccine inoculation pace and create awareness in the population about the importance of COVID-19 vaccines.

Modeling toxoplasmosis spread in cat populations under vaccination.

In this paper we present an epidemiological model to study the transmission dynamics of toxoplasmosis in a cat population under a continuous vaccination schedule. We explore the dynamics of toxoplasmosis at the population level using a mathematical model that includes the effect of oocyst, since the probability of acquisition of Toxoplasma Gondii infection depends on the environmental load of the parasite. This model considers indirectly the infection of prey through the oocyst shedding by cats. We prove that the basic reproduction number R(0) is a threshold value that completely determines the global dynamics and the outcome of the disease. Numerical computer simulations are presented to investigate different scenarios. These simulations show the effectiveness of a constant vaccination program.

A quantitative assessment of dynamical differences of RSV infections in vitro and in vivo.

Experimental results in vitro and in animal models are used to guide researchers in testing vaccines or treatment in humans. However, viral kinetics are different in vitro, in animals, and in humans, so it is sometimes difficult to translate results from one system to another. In this study, we use a mathematical model to fit experimental data from multiple cycle respiratory syncytial virus (RSV) infections in vitro, in african green monkey (AGM), and in humans in order to quantitatively compare viral kinetics in the different systems. We find that there are differences in viral clearance rate, productively infectious cell lifespan, and eclipse phase duration between in vitro and in vivo systems and among different in vivo systems. We show that these differences in viral kinetics lead to different estimates of drug effectiveness of fusion inhibitors in vitro and in AGM than in humans.

A comparison of RSV and influenza in vitro kinetic parameters reveals differences in infecting time.

Influenza and respiratory syncytial virus (RSV) cause acute infections of the respiratory tract. Since the viruses both cause illnesses with similar symptoms, researchers often try to apply knowledge gleaned from study of one virus to the other virus. This can be an effective and efficient strategy for understanding viral dynamics or developing treatment strategies, but only if we have a full understanding of the similarities and differences between the two viruses. This study used mathematical modeling to quantitatively compare the viral kinetics of in vitro RSV and influenza virus infections. Specifically, we determined the viral kinetics parameters for RSV A2 and three strains of influenza virus, A/WSN/33 (H1N1), A/Puerto Rico/8/1934 (H1N1), and pandemic H1N1 influenza virus. We found that RSV viral titer increases at a slower rate and reaches its peak value later than influenza virus. Our analysis indicated that the slower increase of RSV viral titer is caused by slower spreading of the virus from one cell to another. These results provide estimates of dynamical differences between influenza virus and RSV and help provide insight into the virus-host interactions that cause observed differences in the time courses of the two illnesses in patients.

Quantifying rotavirus kinetics in the REH tumor cell line using in vitro data.

Globally, rotavirus is the most common cause of diarrhea in children younger than 5 years of age, however, a quantitative understanding of the infection dynamics is still lacking. In this paper, we present the first study to extract viral kinetic parameters for in vitro rotavirus infections in the REH cell tumor line. We use a mathematical model of viral kinetics to extract parameter values by fitting the model to data from rotavirus infection of REH cells. While accurate results for some of the parameters of the mathematical model were not achievable due to its global non-identifiability, we are able to quantify approximately the time course of the infection for the first time. We also find that the basic reproductive number of rotavirus, which gives the number of secondary infections from a single infected cell, is much greater than one. Quantifying the kinetics of rotavirus leads not only to a better understanding of the infection process, but also provides a method for quantitative comparison of kinetics of different strains or for quantifying the effectiveness of antiviral treatment.

Prediction of the respiratory syncitial virus epidemic using climate variables in Bogotá, D.C.

lntroduction: The respiratory syncitial virus is one of the most common causes of mortality in children and older adults in the world. Objective: To predict the initial week of outbreaks and to establish the most relevant climate variables using naive Bayes classifiers and receiver operating characteristic curves (ROC). Materials and methods: The initial dates of the outbreaks in children less than five years old for the period 2005-2010 were obtained for Bogotá, Colombia. We selected the climatological variables using a correlation matrix and we constructed 1,020 models using different climatological variables and data from different weeks previous to the initial outbreak. In addition, we selected models using a six-year period (2005-2010), a four-year period (2005-2008), and a two-year period (2009-2010). We obtained the best predictive models and the most relevant climatological variables to predict the outbreak using naive Bayes classifiers and ROC curves. Results: The best models were those using a two-year period (2009-2010) and week 0, with 52% and 60% of effectiveness, respectively. Humidity was the most frequent variable in the best models (62%). Conclusions: We used naive Bayes classifiers to establish the best models to predict correctly the initial week of the outbreak. Our results suggest that the best models used humidity, wind speed and minimum temperature in outbreaks prediction.