Bulletin of Mathematical Biology

The rapid rise of antibiotic resistance is a serious threat to global public health. Without further incentives, pharmaceutical companies have little interest in developing antibiotics, since the success probability is low and development costs are huge. The situation is exacerbated by the "antibiotics dilemma": Developing narrow-spectrum antibiotics against resistant bacteria is most beneficial for society, but least attractive for companies since their usage is more limited than for broad-spec...

The global spread of Coronavirus Disease 2019 (COVID-19) is overwhelming many health-care systems. As a result, epidemiological models are being used to inform policy on how to effectively deal with this pandemic. The majority of existing models assume random diffusion but do not take into account differences in the amount of interactions between individuals, i.e. the underlying human interaction network, whose structure is known to be scale-free. Here, we demonstrate how this network of interac...

We present a deterministic, calibrated Susceptible-Exposed-Infected-Recovered-Dead + Vaccinated (SEIRD+V) model that simulates the spread and containment of COVID-19. We use the model to compare the effectiveness of vaccination vs. social distancing on death prevention and total and peak infection reduction. We find that vaccination drastically reduces total deaths from COVID-19, as well as total and peak infections with Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). We find that ...

AO_SCPLOWBSTRACTC_SCPLOWExisting methods to infer the relative roles of age groups in epidemic transmission can normally only accommodate a few age classes, and/or require data that are highly specific for the disease being studied. Here, symbolic transfer entropy (STE), a measure developed to identify asymmetric transfer of information between stochastic processes, is presented as a way to determine which age groups drive an epidemic. STE provides a ranking of which age groups dominate transmis...

As with the Spanish Flu a century ago, authorities have responded to the current COVID-19 pandemic with extraordinary public health measures. In particular, lockdown and related social distancing policies are motivated in some countries by the need to slow virus propagation--so that the primary wave of patients suffering from severe forms of COVID infection do not exceed the capacity of intensive care units. But unlocking poses a critical issue because relaxing social distancing may, in principl...

The COVID-19 pandemic has sparked an intense debate about the factors underlying the dynamics of the outbreak. Mitigating virus spread could benefit from reliable predictive models that inform effective social and healthcare strategies. Crucially, the predictive validity of these models depends upon incorporating behavioral and social responses to infection that underwrite ongoing social and healthcare strategies. Formally, the problem at hand is not unlike the one faced in neuroscience when mod...

We develop a new framework specifically for early Phase I clinical trials called Bayesian Ordered Lattice Design (BOLD). This study is motivated by two key factors. First, Phase I clinical trials typically involve relatively small sample sizes, which can make the use of prior information on dose-limiting toxicity (DLT) rates highly significant. To address this challenge, the proposed Bayesian methodology incorporates prior information and posterior updating to guide dose selection, toxicity moni...

A fundamental problem dealing with the Covid-19 pandemic has been to estimate the rate of infection, since so many cases are asymptomatic and contagious just for a few weeks. For example, in the US, estimate the proportion P(t) = N/330 where N is the US total who have ever been infected (in millions)at time t (months, t = 0 being March 20). This is important for decisions on social restrictions, and allocation of medical resources, etc. However, the demand for extensive testing has not produced ...

In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found, JAK2 V617F and one in the TET2 gene. Whether or not one mutation is present will influence how the other subsequent mutation affects the regulation of gene expression. When both mutations are present, the order of their occurrence has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation (ODE), Moran process, and Markov chain models to explai...

An emerging consensus regarding the triangle relationship between tumor, immune cells, and microbiomes is the immune-oncology-microbiome (IOM) axis, which stipulates that microbiomes can act as a discrete enabling (or disabling) characteristic that broadly influence the acquisition of certain hallmarks of cancer, i.e., a set of functional capabilities acquired by human cells during carcinogenesis and progression to malignant tumors. Specifically, it has been postulated that polymorphic microbiom...

Using standard systems biology methodologies a 14-compartment dynamic model was developed for the Corona virus epidemic. The model predicts that : (i) it will be impossible to limit lockdown intensity such that sufficient herd immunity develops for this epidemic to die down, (ii) the death toll from the SARS-CoV-2 virus decreases very strongly with increasing intensity of the lockdown, but (iii) the duration of the epidemic increases at first with that intensity and then decreases again, such th...

Deterministic epidemic models, such as the Susceptible-Infected-Recovered (SIR) model, are immensely useful even if they lack the nuance and complexity of social contacts at the heart of network science modeling. Here we present a simple modification of the SIR equations to include the heterogeneity of social connection networks. A typical power-law model of social interactions from network science reproduces the observation that individuals with a high number of contacts, "hubs" or "superspread...

The COVID-19 pandemic has caused more than 25 million cases and 800 thousand deaths worldwide to date. Neither vaccines nor therapeutic drugs are currently available for this novel coronavirus. All measures to prevent the spread of COVID-19 are thus based on reducing contact between infected and susceptible individuals. Most of these measures such as quarantine and self-isolation require voluntary compliance by the population. However, humans may act in their (perceived) self-interest only. We c...

Epidemics are nonlinear adaptive processes in which pathogen spread and human behavior form a tightly coupled feedback loop. Individual decisions about protective measures create strategic interactions. These interactions can either accelerate disease spread or drive collective suppression. We introduce a theoretical lattice-based agent model that fuses SIS contagion with an evolutionary game, systematically exploring how strategy choice and infection pressure co-evolve through comprehensive par...

Due to the usage of social distancing as a means to control the spread of the novel coronavirus disease COVID-19, there has been a large amount of research into the dynamics of epidemiological models with time-varying transmission rates. Such studies attempt to capture population responses to differing levels of social distancing, and are used for designing policies which both inhibit disease spread but also allow for limited economic activity. One common criterion utilized for the recent pandem...

Vaccine hesitancy is a major threat to public health. While the root causes of vaccine hesitancy are numerous, they largely revolve around some form of perceived risk to the self. In particular, the unknown long-term risks are amongst the most frequently cited concerns. In this work, we show that regardless of their peak onset following vaccination, the incidence of adverse outcomes will follow some distribution f (x| {micro}, {sigma}2) of mean onset {micro}, and standard deviation{sigma} , and ...

Within the context of SEIR models, we consider a lockdown that is both imposed and lifted at an early stage of an epidemic. We show that, in these models, although such a lockdown may delay deaths, it eventually does not avert a significant number of fatalities. Therefore, in these models, the efficacy of a lockdown cannot be gauged by simply comparing figures for the deaths at the end of the lockdown with the projected figure for deaths by the same date without the lockdown. We provide a simple...

Many countries have passed their first COVID-19 epidemic peak. Traditional epidemiological models describe this as a result of non-pharmaceutical interventions that pushed the growth rate below the recovery rate. In this new phase of the pandemic many countries show an almost linear growth of confirmed cases for extended time-periods. This new containment regime is hard to explain by traditional models where infection numbers either grow explosively until herd immunity is reached, or the epidemi...

AO_SCPLOWBSTRACTC_SCPLOWNewly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raise...

In the event of a global pandemic, caused by an infectious disease of humans, we consider the scenario in which a safe and effective vaccine is available, with limited supply. We then investigate the optimal distribution of doses across countries and age groups. We employ a system of SIR equations to model the pandemic dynamics and utilize genetic algorithms to identify optimal allocations that minimize either total infections or total deaths. Our findings reveal that strategies aimed at reducin...