Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics

Deterministic epidemic models overestimate the basic reproduction number of observed outbreaks

The basic reproduction number, R0, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating R0 from incidence data early in the epidemic can lead to an over-estimation of this quantity. In particular, when fitting deterministic models to estimate the rate of spread, we do not account for the stochastic nature of epidemics and that, given the same system, some outbreaks may lead to epidemics and some may not. Typically, an observed epidemic that we wish to control is a major outbreak. This amounts to implicit selection for major outbreaks which leads to the over-estimation problem. We formally characterised the split between major and minor outbreaks by using Otsu's method which provides us with a working definition. We show that by conditioning a 'deterministic' model on major outbreaks, we can more reliably estimate the basic reproduction number from an observed epidemic trajectory.

Modelling the impact of some control strategies on the transmission dynamics of Ebola virus in human-bat population: An optimal control analysis

Qualitative research and comprehensive public awareness to nip the transmission of Ebola virus in the bud before it becomes a global threat is fast becoming imperative especially now that the Gambia Ebola virus is mutated. It is therefore necessary to consider and investigate a vector-host transmission model for possible control strategy of this deadly disease. Hence, in this study, we presented a novel and feasible human-bat (host-vector) S h E h I h R h i s R h n i - S b E b I b model which foretells the spread and severity of the Ebola virus from bats to humans to investigate the combined effects of three control strategies viz: (1) allowing specialized and designated agencies to bury deceased from Ebola infection without relatives touching or curdling the remains as usually practiced in most part of Africa as last respect for their departed love ones ( k 1 ), (2) systematic and deliberate depopulation of bats in the metropolis (through persecution with pesticide exposure, pre capturing, chemical timber treatment for roosts destruction) to discourage hunting them for food by virtue of their proximity ( k 2 ) and (3) immediate treatment of infected individuals in isolation ( k 3 ). We established, among others, the endemic equilibrium, disease-free equilibrium, global and local stability, non-negativity, and boundedness of the model to prove the epidemiological feasibility of the model. The reality of the presence of optimal control remarkably influences the dynamics of transmission of the virus and simulated results also confirm the great effect of the combination of the control strategies k 1 , k 2 and k 3 in flattening the curve of Ebola transmission (fig 1 - fig 8). Health workers and policy makers are better informed with fundamental precautions that could help eradicate Ebola from the populace.

More can be better: An analysis of single-mutant fixation probability functions under 2 × 2 games

Evolutionary game theory has proved to be a powerful tool to probe the self-organization of collective behaviour by considering frequency-dependent fitness in evolutionary processes. It has shown that the stability of a strategy depends not only on the payoffs received after each encounter but also on the population’s size. Here, we study 2 × 2 games in well-mixed finite populations by analyzing the fixation probabilities of single mutants as functions of population size. We proved that nine of the 24 possible games always lead to monotonically decreasing functions, similarly to fixed fitness scenarios. However, fixation functions showed increasing regions under 12 distinct anti-coordination, coordination and dominance games. Perhaps counter-intuitively, this establishes that single-mutant strategies often benefit from being in larger populations. Fixation functions that increase from a global minimum to a positive asymptotic value are pervasive but may have been easily concealed by the weak selection limit. We obtained sufficient conditions to observe fixation increasing for small populations and three distinct ways this can occur. Finally, we describe fixation functions with the increasing regions bounded by two extremes under intermediate population sizes. We associate their occurrence with transitions from having one global extreme to other shapes.