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COVID-19 highlighted the importance of considering human behavior change when modeling disease dynamics. This led to developing various models that incorporate human behavior. Our objective is to contribute to an in-depth, mathematical examination of such models. Here, we consider a simple deterministic compartmental model with endogenous incorporation of human behavior (i.e., behavioral feedback) through transmission in a classic Susceptible–Exposed–Infectious–Recovered (SEIR) structure. Despite its simplicity, the SEIR structure with behavior (SEIRb) was shown to perform well in forecasting, especially compared to more complicated models. We contrast this model with an SEIR model that excludes endogenous incorporation of behavior. Both models assume permanent immunity to COVID-19, so we also consider a modification of the models which include waning immunity (SEIRS and SEIRSb). We perform equilibria, sensitivity, and identifiability analyses on all models and examine the fidelity of the models to replicate COVID-19 data across the United States. Endogenous incorporation of behavior significantly improves a model’s ability to produce realistic outbreaks. While the two endogenous models are similar with respect to identifiability and sensitivity, the SEIRSb model, with the more accurate assumption of the waning immunity, strengthens the initial SEIRb model by allowing for the existence of an endemic equilibrium, a realistic feature of COVID-19 dynamics. When fitting the model to data, we further consider the addition of simple seasonality affecting disease transmission to highlight the explanatory power of the models. 

One-dimensional discrete-time population models, such as those that involve Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Expanding the system by one dimension to incorporate epidemiological interactions causes an interesting complexity of new behaviors. Here, we examine a discrete-time two-dimensional susceptible-infectious (SI) model with Ricker growth and show that the introduction of infection can not only produce a distinctly different bifurcation structure than that of the underlying disease-free system but also lead to counter-intuitive increases in population size. We use numerical bifurcation analysis to determine the influence of infection on the location and types of bifurcations. In addition, we examine the appearance and extent of a phenomenon known as the ‘hydra effect,’ i.e., increases in total population size when factors, such as mortality, that act negatively on a population, are increased. Previous work, primarily focused on dynamics at fixed points, showed that the introduction of infection that reduces fecundity to the SI model can lead to a so-called ‘infection-induced hydra effect.’ Our work shows that even in such a simple two-dimensional SI model, the introduction of infection that alters fecundity or mortality can produce dynamics can lead to the appearance of a hydra effect, particularly when the disease-free population is at a cycle.

 

In the first two years of the COVID-19 pandemic, per capita mortality varied by more than a hundredfold across countries, despite most implementing similar nonpharmaceutical interventions. Factors such as policy stringency, gross domestic product, and age distribution explain only a small fraction of mortality variation. To address this puzzle, we built on a previously validated pandemic model in which perceived risk altered societal responses affecting SARS-CoV-2 transmission. Using data from more than 100 countries, we found that a key factor explaining heterogeneous death rates was not the policy responses themselves but rather variation in responsiveness. Responsiveness measures how sensitive communities are to evolving mortality risks and how readily they adopt nonpharmaceutical interventions in response, to curb transmission. We further found that responsiveness correlated with two cultural constructs across countries: uncertainty avoidance and power distance. Our findings show that more responsive adoption of similar policies saves many lives, with important implications for the design and implementation of responses to future outbreaks. 

Abstract Background Mosquitoes are vectors for diseases such as dengue, malaria and La Crosse virus that significantly impact the human population. When multiple mosquito species are present, the competition between species may alter population dynamics as well as disease spread. Two mosquito species, Aedes albopictus and Aedes triseriatus , both inhabit areas where La Crosse virus is found. Infection of Aedes albopictus by the parasite Ascogregarina taiwanensis and Aedes triseriatus by the parasite Ascogregarina barretti can decrease a mosquito’s fitness, respectively. In particular, the decrease in fitness of Aedes albopictus occurs through the impact of Ascogregarina taiwanensis on female fecundity, larval development rate, and larval mortality and may impact its initial competitive advantage over Aedes triseriatus during invasion. Methods We examine the effects of parasitism of gregarine parasites on Aedes albopictus and triseriatus population dynamics and competition with a focus on when Aedes albopictus is new to an area. We build a compartmental model including competition between Aedes albopictus and triseriatus while under parasitism of the gregarine parasites. Using parameters based on the literature, we simulate the dynamics and analyze the equilibrium population proportion of the two species. We consider the presence of both parasites and potential dilution effects. Results We show that increased levels of parasitism in Aedes albopictus will decrease the initial competitive advantage of the species over Aedes triseriatus and increase the survivorship of Aedes triseriatus . We find Aedes albopictus is better able to invade when there is more extreme parasitism of Aedes triseriatus . Furthermore, although the transient dynamics differ, dilution of the parasite density through uptake by both species does not alter the equilibrium population sizes of either species. Conclusions Mosquito population dynamics are affected by many factors, such as abiotic factors (e.g. temperature and humidity) and competition between mosquito species. This is especially true when multiple mosquito species are vying to live in the same area. Knowledge of how population dynamics are affected by gregarine parasites among competing species can inform future mosquito control efforts and help prevent the spread of vector-borne disease. 

Mosquitoes vector harmful pathogens that infect millions of people every year, and developing approaches to effectively control mosquitoes is a topic of great interest. However, the success of many control measures is highly dependent upon ecological, physiological, and life history traits of mosquito species. The behavior of mosquitoes and their potential to vector pathogens can also be impacted by these traits. One trait of interest is mosquito body mass, which depends upon many factors associated with the environment in which juvenile mosquitoes develop. Our experiments examined the impact of larval density on the body mass of Aedes aegypti mosquitoes, which are important vectors of dengue, Zika, yellow fever, and other pathogens. To investigate the interactions between the larval environment and mosquito body mass, we built a discrete time mathematical model that incorporates body mass, larval density, and food availability and fit the model to our experimental data. We considered three categories of model complexity informed by data, and selected the best model within each category using Akaike’s Information Criterion. We found that the larval environment is an important determinant of the body mass of mosquitoes upon emergence. Furthermore, we found that larval density has greater impact on body mass of adults at emergence than on development time, and that inclusion of density dependence in the survival of female aquatic stages in models is important. We discuss the implications of our results for the control of Aedes mosquitoes and on their potential to spread disease. 

Successful infectious disease interventions can result in large reductions in parasite prevalence. Such demographic change has fitness implications for individual parasites and may shift the parasite’s optimal life history strategy. Here, we explore whether declining infection rates can alter Plasmodium falciparum ’s investment in sexual versus asexual growth. Using a multiscale mathematical model, we demonstrate how the proportion of polyclonal infections, which decreases as parasite prevalence declines, affects the optimal sexual development strategy: Within-host competition in multiclone infections favors a greater investment in asexual growth whereas single-clone infections benefit from higher conversion to sexual forms. At the same time, drug treatment also imposes selection pressure on sexual development by shortening infection length and reducing within-host competition. We assess these models using 148 P. falciparum parasite genomes sampled in French Guiana over an 18-y period of intensive intervention (1998 to 2015). During this time frame, multiple public health measures, including the introduction of new drugs and expanded rapid diagnostic testing, were implemented, reducing P. falciparum malaria cases by an order of magnitude. Consistent with this prevalence decline, we see an increase in the relatedness among parasites, but no single clonal background grew to dominate the population. Analyzing individual allele frequency trajectories, we identify genes that likely experienced selective sweeps. Supporting our model predictions, genes showing the strongest signatures of selection include transcription factors involved in the development of P. falciparum ’s sexual gametocyte form. These results highlight how public health interventions impose wide-ranging selection pressures that affect basic parasite life history traits. 

Abstract We employ individual-based Monte Carlo computer simulations of a stochastic SEIR model variant on a two-dimensional Newman–Watts small-world network to investigate the control of epidemic outbreaks through periodic testing and isolation of infectious individuals, and subsequent quarantine of their immediate contacts. Using disease parameters informed by the COVID-19 pandemic, we investigate the effects of various crucial mitigation features on the epidemic spreading: fraction of the infectious population that is identifiable through the tests; testing frequency; time delay between testing and isolation of positively tested individuals; and the further time delay until quarantining their contacts as well as the quarantine duration. We thus determine the required ranges for these intervention parameters to yield effective control of the disease through both considerable delaying the epidemic peak and massively reducing the total number of sustained infections. 

Some infectious diseases produce lifelong immunity while others only produce temporary immunity. In the case of short-lived immunity, the level of protection wanes over time and may be boosted upon re-exposure, via infection or vaccination. Previous work developed a simple model capturing waning and boosting immunity, known as the Susceptible-Infectious-Recovered-Waned-Susceptible (SIRWS) model, which exhibits rich dynamical behavior including supercritical and subcritical Hopf bifurcations among other structures. Here, we extend the bifurcation analyses of the SIRWS model to examine the influence of all parameters on these bifurcation structures. We show that the bistable region, involving both a stable fixed point and a stable limit cycle, exists only for a small region of biologically realistic parameter space. Furthermore, we contrast the SIRWS model with a modified version, where immune boosting may involve the occurrence of a secondary infection. Analysis of this extended model shows that oscillations and bistability, as found in the SIRWS model, depend on strong assumptions about infectivity and recovery rate from secondary infection. Understanding the dynamics of models of waning and boosting immunity is important for accurately assessing epidemiological data.