Journal of Theoretical Biology

Due to the current COVID-19 epidemic plague hitting the worldwide population it is of utmost medical, economical and societal interest to gain reliable predictions on the temporal evolution of the spreading of the infectious diseases in human populations. Of particular interest are the daily rates and cumulative number of new infections, as they are monitored in infected societies, and the influence of non-pharmaceutical interventions due to different lockdown measures as well as their subsequen...

In this paper we develop a generalization of the Kermack-McKendrick SIR model where the time of infectiousness follows the Weibull distribution. We compute the equivalent classical results available for the classical SIR model, particularly a general expression for the basic reproduction number. We comment about the implications of this generalization in epidemic and metapopulation dynamics and illustrate our findings with some numerical simulations.

Recently, [8] has proposed that heterogeneity of infectiousness (and susceptibility) across individuals in infectious diseases, plays a major role in affecting the Herd Immunity Thresh-old (HIT). Such heterogeneity has been observed in COVID-19 and is recognized as overdis-persion (or "super-spreading"). The model of [8] suggests that super-spreaders contribute significantly to the effective reproduction factor, R, and that they are likely to get infected and immune early in the process. Consequ...

AO_SCPLOWBSTRACTC_SCPLOWCompartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this disease and others like it, such as the ability of exposed individuals to recover without becoming infectious, or the possibility that asymptomatic individuals can indeed transmit the disease but at a lesser rate than the symptomatic. Furt...

Sequel to [10], who studied the dynamics of COVID-19 using an SEIRUS model. We consider an SEIRS model capturing saturated incidence with treatment response. In this theoretical model, we assumed that the treatment response is proportional to the number of infected as long as the incidence cases are within the capacity of the healthcare system, after which the value becomes constant, when the number of confirmed cases exceed the carrying capacity of the available medical facilities. Thus, we obt...

In this article we propose a compartmental model for the dynamics of Coronavirus Disease 2019 (COVID-19). We take into account the presence of asymptomatic infections and the main policies that have been adopted so far to contain the epidemic: isolation (or social distancing) of a portion of the population, quarantine for confirmed cases and testing. We model isolation by separating the population in two groups: one composed by key-workers that keep working during the pandemic and have a usual c...

The interaction and possibly interference between viruses infecting a host population is addressed in this work. We model two viral diseases with a similar transmission mechanism and for which a vaccine exists. The vaccine is characterized by its coverage, induced temporary immunity, and efficacy. The population dynamics of both diseases consider infected individuals of each illness and hosts susceptible to one but recovered from the other. We do not incorporate co-infection. Two main transmissi...

The current global outbreaks of Monkeypox is a unique infectious disease in the way it seems to be transmitting: it has been observed to be highly concentrated in communities of men who have sex with men (MSM) through pair formation, and also provides immunity. This framework of mostly close, prolonged contact spreading a disease that admits immunity after infection is unlike similar infections which either offer little to no immunity post-infection or are lifelong infections. This creates the n...

A simple two-cohort SIR like model can explain the qualitative behaviour of the logarithmic derivative estimations of the covid-19 epidemic evolution as observed in several countries. The model consists of a general population in which the R0 value is slightly below 1, but in which a super-spreading small subgroup with high R0, coupled to the general population, is contaminating a significant fraction of the population. The epidemic starts to slow down when herd immunity is reached in this subgr...

In this manuscript, we derive a closed form solution to the full Kermack and McKendrick integro-differential equations (Kermack and McKendrick 1927) which we call the KMES. We demonstrate the veracity of the KMES using independent data from the Covid 19 pandemic and derive many previously unknown and useful analytical expressions for characterizing and managing an epidemic. These include expressions for the viral load, the final size, the effective reproduction number, and the time to the peak i...

The purpose of this work is to make a case for epidemiological models with fractional exponent in the contribution of sub-populations to the transmission rate. More specifically, we question the standard assumption in the literature on epidemiological models, where the transmission rate dictating propagation of infections is taken to be proportional to the product between the infected and susceptible sub-populations; a model that relies on strong mixing between the two groups and widespread cont...

The reproduction number R, the average number of people that a single individual with a contagious disease infects, is central to understanding the dynamics of the COVID-19 epidemic. Values greater than one correspond to increasing rates of infection, and values less than one indicate that control measures are being effective. Here, we summarise how changes in the behaviour of individuals alter the value of R. We also use matrix models that correctly recreate distributions of times that individu...

(Dated: September 6, 2020) A well-known characteristic of pandemics such as COVID-19 is the high level of transmission heterogeneity in the infection spread: not all infected individuals spread the disease at the same rate and some individuals (superspreaders) are responsible for most of the infections. To quantify this phenomenon requires the analysis of the effect of the variance and higher moments of the infection distribution. Working in the framework of stochastic branching processes, we d...

The concern about (socio-)economic consequences of collective lockdowns in the Covid-19 pandemic calls for alternative strategies. We consider a divide and conquer strategy in which a high risk group (HRG) is put on strict isolation, whereas the remainder of the population is exposed to the virus, building up immunity against Covid-19. The question is whether this strategy may suppress the effective reproduction number below the critical value of [Formula] without further lockdown once the HRG i...

The effective reproduction ratio r(t) of an epidemic, defined as the average number of secondary infected cases per infectious case in a population in the current state, including both susceptible and non-susceptible hosts, controls the transition between a subcritical threshold regime (r(t) < 1) and a supercritical threshold regime (r(t) > 1). While in subcritical regimes, an index infected case will cause an outbreak that will die out sooner or later, with large fluctuations observed when appr...

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. 2. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with p-bran...

We constructed a simple Susceptible-Infected-Infectious-Excluded model of the spread of COVID-19. The model is parametrised only by the average incubation period,{tau} , and two rate parameters: contact rate, rC, and exclusion rate, rE. The rates can be manipulated by non-therapeutic interventions and determine the basic reproduction number, R = rC/rE, and, together with{tau} , the daily multiplication coefficient at the early exponential phase, {beta}. Initial {beta} determines the reduction of...

Many countries have introduced Lockdowns to contain the COVID19 epidemic. Lockdowns, though an effective policy for containment, imposes a heavy cost on the economy as it enforces extreme social distancing measures on the whole population. The objective of this note is to study alternatives to Lockdown which are either more targeted or allows partial opening of the economy. Cities are often spatially organized into wards. We introduce Multi-lattice small world (MLSW) network as a model of a city...

We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The control is allowed to be applied only over a finite time interval, while the objective is to minimize the total number of individuals infected in the long-time limit, subject to some cost function for the control. We first consider the no-cost scenario and analytica...

The birth and death of a pandemic can be region specific. Pandemic seems to make repeated appearance in some places which is often attributed to human neglect and seasonal change. However, difference could arise from different distributions of inherent susceptibility ({sigma}inh) and external infectivity ({iota}ext) from one population to another. These are often ignored in the theoretical treatments of an infectious disease progression. While the former is determined by the immunity of an indiv...