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The COVID-19 pandemic has presented unprecedented challenges worldwide, necessitating effective modelling approaches to understand and control its transmission dynamics. In this study, we propose a novel approach that integrates asymptomatic and super-spreader individuals in a single compartmental model. We highlight the advantages of utilizing incommensurate fractional order derivatives in ordinary differential equations, including increased flexibility in capturing disease dynamics and refined memory effects in the transmission process. We conduct a qualitative analysis of our proposed model, which involves determining the basic reproduction number and analysing the disease-free equilibrium's stability. By fitting the proposed model with real data from Portugal and comparing it with existing models, we demonstrate that the incorporation of supplementary population classes and fractional derivatives significantly improves the model's goodness of fit. Sensitivity analysis further provides valuable insights for designing effective strategies to mitigate the spread of the virus. • Asymptomatic and super-spreader individuals. • Innovative approach to modelling COVID-19 transmission dynamics. • Qualitative analysis, basic reproduction number, equilibrium and sensitivity analysis. • Benefits of incommensurate fractional order derivatives. • Memory effects in the transmission process, Real data from Portugal. [ABSTRACT FROM AUTHOR]

Containing infectious disease outbreaks is a complex challenge that usually requires the deployment of multiple intervention strategies. While mathematical modeling of infectious diseases is a widely accepted tool to evaluate intervention strategies, most models and studies overlook the interdependence between individuals' reactions to simultaneously implemented interventions. Intervention modeling efforts typically assume that individual adherence decisions are independent of each other. However, in the real world, individuals who are willing to comply with certain interventions may be more or less likely to comply with another intervention. The combined effect of interventions may depend on the correlation between adherence decisions. In this study, we consider vaccination and non-pharmaceutical interventions, and study how the correlation between individuals' behaviors towards these two interventions strategies affects the epidemiological outcomes. Furthermore, we integrate disease surveillance in our model to study the effects of interventions triggered by surveillance events. This allows us to model a realistic operational context where surveillance informs the timing of interventions deployment, thereby influencing disease dynamics. Our results demonstrate the diverse effects of coupled individual behavior and highlight the importance of robust surveillance systems. Our study yields the following insights: (i) there exists a correlation level that minimizes the initial prevalence peak size; (i i) the optimal correlation level depends on the disease's basic reproduction number; (i i i) disease surveillance modulates the impact of interventions on reducing the epidemic burden. • Individual adherence decisions to multiple epidemic interventions can be correlated. • This correlation affects epidemic dynamics and combined intervention effectiveness. • It should be integrated in disease models involving multiple interventions. • Disease surveillance modulates the impact of interventions on the epidemic burden. [ABSTRACT FROM AUTHOR]

Alveolar echinococcosis, transmitted between definitive hosts and intermediate hosts via predation, threatens the health of humans and causes great economic losses in western China. In order to explore the transmission mechanism of this disease, an eco-epidemiological lifecycle model is formulated to illustrate interactions between two hosts. The basic and demographic reproduction numbers are developed to characterize the stability of the disease-free and endemic equilibria as well as bifurcation dynamics. The existence of forward bifurcation and Hopf bifurcation are confirmed and are used to explain the threshold transmission dynamics. Numerical simulations and bifurcation diagrams are also presented to depict rich dynamics of the model. Numerical analysis suggests that improving the control rate of voles will reduce the risk of transmission, while the high predation rate of foxes may also lead to a lower transmission risk, which is different from the predictions of previous studies. The evaluation of three control measures on voles implies that, when the fox's predation rate is low (high), the chemical (integrated) control will be more effective. • The new eco-epidemiological model provides a reasonable explanation of AE transmission mechanism. • Analysis for bifurcations reveal that the model exhibits rich dynamics. • Sensitive analysis indicates that a higher predation rate of foxes does not mean a higher transmission risk. • High control rate of voles is necessary to eradicate the disease. [ABSTRACT FROM AUTHOR]

Based on the distinctive spatial diffusion characteristics observed in syphilis transmission patterns, this paper introduces a novel reaction–diffusion model for syphilis disease dynamics, incorporating general incidence functions within a heterogeneous environment. We derive the basic reproduction number essential for threshold dynamics and investigate the uniform persistence of the model. We validate the model and estimate its parameters by employing the multi-objective Markov Chain Monte Carlo (MCMC) method, using real syphilis data from the years 2004 to 2018 in China. Furthermore, we explore the impact of spatial heterogeneity and intervention measures on syphilis transmission. Our findings reveal several key insights: (1) In addition to the original high-incidence areas of syphilis, Xinjiang, Guizhou, Hunan and Northeast China have also emerged as high-incidence regions for syphilis in China. (2) The latent syphilis cases represent the highest proportion of newly reported cases, highlighting the critical importance of considering their role in transmission dynamics to avoid underestimation of syphilis outbreaks. (3) Neglecting spatial heterogeneity results in an underestimation of disease prevalence and the number of syphilis-infected individuals, undermining effective disease prevention and control strategies. (4) The initial conditions have minimal impact on the long-term spatial distribution of syphilis-infected individuals in scenarios of varying diffusion rates. This study underscores the significance of spatial dynamics and intervention measures in assessing and managing syphilis transmission, which offers insights for public health policymakers. • Formulating a reaction-diffusion model to understand spatiotemporal syphilis dynamics • Validating the model using real syphilis data • Uncovering new high-incidence regions beyond the original hotspots • Emphasizing the significance of latent stage in syphilis transmission • Testing intervention measures for effective syphilis containment strategies [ABSTRACT FROM AUTHOR]

In addition to the traditional transmission route via the biting-and-defecating process, non-human host predation of triatomines is recognized as another significant avenue for Chagas disease transmission. In this paper, we develop an eco-epidemiological model to investigate the impact of predation on the disease's spread. Two critical thresholds, R v p (the basic reproduction number of triatomines) and R 0 p (the basic reproduction number of the Chagas parasite), are derived to delineate the model's dynamics. Through the construction of appropriate Lyapunov functions and the application of the Bendixson–Dulac theorem, the global asymptotic stabilities of the equilibria are fully established. The vector-free equilibrium E 0 is globally stable when R v p < 1. E 1 , the disease-free equilibrium, is globally stable when R v p > 1 and R 0 p < 1 , while the endemic equilibrium E ∗ is globally stable when both R v p > 1 and R 0 p > 1. Numerical simulations highlight that the degree of host predation on triatomines, influenced by non-human hosts activities, can variably increase or decrease the Chagas disease transmission risk. Specifically, low or high levels of host predation can reduce R 0 p to below unity, while intermediate levels may increase the infected host populations, albeit with a reduction in R 0 p. These findings highlight the role played by non-human hosts and offer crucial insights for the prevention and control of Chagas disease. • A novel model integrating systemic and non-human predation transmission is developed. • Two thresholds of R v p and R 0 p are derived to delineate the model dynamics. • The global stabilities of the equilibria for the high-dimensional model are shown. • The work offers the crucial insight for the prevention and control of Chagas disease. [ABSTRACT FROM AUTHOR]

We consider compartmental models of communicable disease with uncertain contact rates. Stochastic fluctuations are often added to the contact rate to account for uncertainties. White noise, which is the typical choice for the fluctuations, leads to significant underestimation of the disease severity. Here, starting from reasonable assumptions on the social behavior of individuals, we model the contacts as a Markov process which takes into account the temporal correlations present in human social activities. Consequently, we show that the mean-reverting Ornstein–Uhlenbeck (OU) process is the correct model for the stochastic contact rate. We demonstrate the implication of our model on two examples: a Susceptibles–Infected–Susceptibles (SIS) model and a Susceptibles–Exposed–Infected–Removed (SEIR) model of the COVID-19 pandemic and compare the results to the available US data from the Johns Hopkins University database. In particular, we observe that both compartmental models with white noise uncertainties undergo transitions that lead to the systematic underestimation of the spread of the disease. In contrast, modeling the contact rate with the OU process significantly hinders such unrealistic noise-induced transitions. For the SIS model, we derive its stationary probability density analytically, for both white and correlated noise. This allows us to give a complete description of the model's asymptotic behavior as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the SEIR model, where the probability density is not available in closed form, we study the transitions using Monte Carlo simulations. Our modeling approach can be used to quantify uncertain parameters in a broad range of biological systems. • New modeling approach taking into account temporal correlations in the contact rate. • Ornstein–Uhlenbeck (OU) process emerges naturally as the model for uncertainties. • Demonstrating the efficacy of our model on an SIS model and data from COVID-19 cases. • Analytical stationary probability density for the SIS model. • A complete description of the models' asymptotic behavior. [ABSTRACT FROM AUTHOR]

Highlights • The study investigates the heterogeneity of the malaria prevalence in South Sudan using a climate-based model. The model is calibrated in a Bayesian framework using Bayesian Markov Chain Monte Carlo (MCMC) in order to allow for a computational simulation of the dynamics that provides an accurate prediction of the reactions. • The study demonstrates the impact of temperature and rainfall on the malaria prevalence in South Sudan. It shows that mosquito population increases in size when mean temperature and rainfall values lie in the range 25–30° C and 20–30 mm, respectively. It also indicates that low or excessive rainfall diminishes mosquito reproduction rate. Abstract Malaria is endemic in South Sudan and it is one of the most severe diseases in the war-torn nation. There has been much concern about whether the severity of its transmission might depend upon climatic conditions that are related to the reproduction of the single-cell parasite attaching to female mosquitoes, especially in high altitude areas. The country experiences two different climatic conditions; namely one tropical and the other hot and semi-arid. In this study, we aim to assess the potential impact of climatic conditions on malaria prevalence in these two climatically distinct regions of South Sudan. We develop and analyze a host-mosquito disease-based model that includes temperature and rainfall. The model has also been parameterized in a Bayesian framework using Bayesian Markov Chain Monte Carlo (MCMC). The mathematical analysis for this study has included equilibria, stability and a sensitivity index on the basic reproduction number R 0. The threshold R 0 is also used to provide a numerical basis for further refinement and prediction of the impact of climate variability on malaria transmission intensity over the study region. The study highlights the impact of various temperature values on the population dynamics of the mosquito. [ABSTRACT FROM AUTHOR]

A dynamic model is proposed to describe a mycoloop in aquatic food webs. The model consists of phytoplankton, chytrids and zooplankton. It characterizes that zooplankton consume both phytoplankton and free-living chytrid spores, and that chytrids infect phytoplankton. The dynamics of the model are investigated containing the dissipativity, existence and stability of equilibria, and persistence. The ecological reproductive indexes for phytoplankton or zooplankton invasion and basic reproduction numbers for chytrid transmission are derived. The parameter values of the model are estimated based on experimental data. Numerical simulations explore the effects of the mycoloop on phytoplankton blooms and chytrid transmission. This research reveals that the mycoloop structure increases or reduces phytoplankton blooms, and controls the spread of chytrids among phytoplankton. • A dynamic model incorporating the effect of mycoloop is derived and analyzed. • Ecological reproductive index plays a key role in dynamical characterization. • The parameter values of the model are estimated based on experimental data. • The effect of mycoloop structure on spread of chytrids is well investigated. • The effect of mycoloop structure on phytoplankton blooms is fully studied. [ABSTRACT FROM AUTHOR]

Highlights • A mathematical model of dengue outbreak in Peshawar, Pakistan is considered. • Model formulations and its basic properties are presented. • Sensitivity analysis and optimal control problem is formulated and discussed • Control strategies are presented for disease elimination. Abstract This paper presents a deterministic model for dengue virus transmission. The model is parameterized using data from the 2017 dengue outbreak in Pakistan. We estimated the basic reproduction number (R 0) without any interventions for the 2017 dengue outbreak in Peshawar district of Pakistan as R 0 ≈ 2.64 , the distribution of the reproduction number lies in the range R 0 ∈ [ 1.21 , 5.24 ] (with a mean R 0 ≈ 2.64). Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using two time-dependent control variables determined from sensitivity analysis. These control variables are insecticide use and vaccination. The results show that the two controls avert the same number of infections in the district regardless of the weights on the costs this is due to the reciprocal relationship between the cost of insecticide use and vaccination. A strong reciprocal relationship exists between the use of insecticide and vaccination; as the cost of insecticide increases the use of vaccination increases. The use of insecticide on the other hand slightly increases when vaccination level decreases due to increase in cost. [ABSTRACT FROM AUTHOR]

Echinococcosis has been recognized as one of the most important helminth zoonosis in China. Available models always consider dogs as the mainly definitive hosts. However, such models ignore the distinctions between domestic dogs and stray dogs. In this study, we propose a 10-dimensional dynamic model distinguishing stray dogs from domestic dogs to explore the special role of stray dogs and potential effects of disposing stray dogs on the transmission of Echinococcosis. The basic reproduction number R 0 , which measures the impact of both domestic dogs and stray dogs on the transmission, is determined to characterize the transmission dynamics. Global dynamic analysis of the model reveals that, without disposing the stray dogs, the Echinococcosis becomes endemic even the domestic dogs are controlled. Moreover, due to the difficulties in estimating the parameters involved in R 0 with real data and the limitation of R 0 in real-world applications, a new risk assessment tool called relative risk index I r i s k is defined for the control of zoonotic diseases, and the studies of the risk assessment for Echinococcosis infection show that it is essential to distinguish stray dogs from domestic dogs in applications. [ABSTRACT FROM AUTHOR]

The bacteria Vibrio cholerae relies heavily upon an aquatic reservoir as a transmission route with two distinct serotypes observed in many recent outbreaks. In this paper, we extend previously studied ordinary differential equation epidemiological models to create a two-strain S I R P (susceptible-infectious-recovered-pathogen) system which incorporates both partial cross-immunity between disease strains and environmental pathogen transmission. Of particular interest are undamped anti-phase periodic solutions, as these display a type of coexistence where strains routinely switch dominance, and understanding what drives this switch can optimize the efficiency of the host population's control measures against the disease. We derive the basic reproduction number R 0 and use stability analysis to examine the disease free and single-strain equilibria. We formulate a unique coexistence equilibrium and prove uniform persistence of both strains when R 0 > 1. In addition, we simulate solutions to this system, along with seasonally forced versions of the model with and without host coinfection. Cross-immunity and transmission pathways influence damped or sustained oscillatory dynamics, where the presence of seasonality can modify, amplify or synchronize the period and phase of serotypes, driving epidemic waves. Cycling of serotypes over large time intervals, similar to observed data, is found for a range of cross-immunity levels, and the inclusion of coinfection in the model contributes to sustained anti-phase periodic solutions. • Model environmental transmission of two cholera serotypes. • Partial cross-immunity impacts coexistence and cycling of serotypes. • Environmental seasonality induces transient and sustained oscillations. • Cross-immunity and environmental transmission affect distinct serotype outbreaks. [ABSTRACT FROM AUTHOR]

One mode by which infection-derived immunity fails is when recovery leads to a reduced but nonzero risk of reinfection. This type of partial protection is called leaky immunity with the degree of leakiness quantified by the relative probability a previously infected individual will get infected upon exposure compared to a naively susceptible individual. Previous authors have defined the reinfection threshold, which occurs when the basic reproduction number equals the inverse of the leakiness, however, there has been some debate about whether or not this is a real threshold. Here we show how the reinfection threshold relates to two important occurrences: (1) the point at which the endemic equilibrium changes from being a stable spiral to a stable node, and (2) the point at which the rate of change of the prevalence increases the most relative to leakiness. When the recovery period is short relative to the average lifetime then both occurrences are close to the reinfection threshold. We show how these results are related to the reinfection threshold found in other models of imperfect immunity. To further demonstrate the significance of this threshold in modeling, we conducted a simulation study to evaluate some of the consequences the reinfection threshold might have in parameter estimation and modeling. Using specific parameter values chosen to reflect an acute infection, we found that the basic reproduction number values larger than that of the reinfection threshold value were less identifiable than those below the threshold. • Dynamical and quantitative changes occur near the reinfection threshold. • The reinfection threshold is especially relevant in models of acute infections. • The reinfection threshold may have an effect on parameter identifiability. [ABSTRACT FROM AUTHOR]

The intrinsic dynamics of bacteria often play an important role in the transmission and spread of waterborne infectious diseases. In this paper, we construct mathematical models for waterborne infections and analyze two types of nontrivial bacterial dynamics: logistic growth, and growth with Allee effects. For the model with logistic growth, we find that regular threshold dynamics take place, and the basic reproduction number can be used to characterize disease extinction and persistence. In contrast, the model with Allee effects exhibits much more complex dynamics, including the existence of multiple endemic equilibria and the presence of backward bifurcation and forward hysteresis. [ABSTRACT FROM AUTHOR]

In this paper, SEIRS epidemiological model with disease caused death and varying total population size is discussed. Based on the geometric approach developed by Li and Muldowney, a new criterion to determine the global asymptotic stability for nonlinear system is proposed. By applying this new criterion, global asymptotic stability of the endemic equilibrium when it is unique is proved. The above global result shows that the basic reproduction number is a sharp threshold for SEIRS model which removes restrictions of rate of loss of immunity and rate of disease caused death in Li and Muldowney’s result. [ABSTRACT FROM AUTHOR]

We introduce and analyze coupled, multi-strain epidemic models designed to simulate the emergence and dissemination of mutant (e.g. drug-resistant) pathogen strains. In particular, we investigate the mathematical and biological properties of a general class of multi-strain epidemic models in which the infectious compartments of each strain are coupled together in a general manner. We derive explicit expressions for the basic reproduction number of each strain and highlight their importance in regulating the system dynamics (e.g. the potential for an epidemic outbreak) and the existence of nonnegative endemic solutions. Importantly, we find that the basic reproduction number of each strain is independent of the mutation rates between the strains — even under quite general assumptions for the form of the infectious compartment coupling. Moreover, we verify that the coupling term promotes strain coexistence (as an extension of the competitive exclusion principle) and demonstrate that the strain with the greatest reproductive capacity is not necessarily the most prevalent. Finally, we briefly discuss the implications of our results for public health policy and planning. [ABSTRACT FROM AUTHOR]

Leishmaniasis is a parasite disease transmitted by the bites of sandflies. Cutaneous leishmaniasis is the most common form of the disease and it is endemic in the Americas. Around 70 animal species, including humans, have been found as natural reservoir hosts of leishmania parasites. Among the reservoirs, dogs are the most important ones due to their proximity to the human habitat. Infection by leishmaniasis does not invariably cause illness in the host, and it also can remain asymptomatic for a long period, specially in dogs. In this work we formulate a model to study the transmission of the disease among the vector, humans and dogs. Our main objective is to asses the impact of dogs as a reservoir as well as the impact of asymptomatic humans and dogs on the spread of leishmaniasis. For this end we calculate the Basic Reproduction Number of the disease and we carry out sensitivity analysis of this parameter with respect to the epidemiological and demographic parameters. [ABSTRACT FROM AUTHOR]

Motivated by studies warning about a possible re-emergence of poliomyelitis in Europe, we analyse a compartmental model for the transmission of polio describing the possible effect of unvaccinated people arriving to a region with low vaccination coverage. We calculate the basic reproduction number, and determine the global dynamics of the system: we show that, depending on the parameters, one of the two equilibria is globally asymptotically stable. The main tools applied are Lyapunov functions and persistence theory. We illustrate the analytic results by numerical examples, which also suggest that in order to avoid the risk of polio re-emergence, vaccinating the immigrant population might result insufficient, and also the vaccination coverage of countries with low rates should be increased. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a malaria model with an asymptomatic class in human population and exposed classes in both human and vector populations. The model assumes that asymptomatic individuals can get re-infected and move to the symptomatic class. In the case of an incomplete treatment, symptomatic individuals move to the asymptomatic class. If successfully treated, the symptomatic individuals recover and move to the susceptible class. The basic reproduction number, R 0 , is computed using the next generation approach. The system has a disease-free equilibrium (DFE) which is locally asymptomatically stable when R 0 < 1 , and may have up to four endemic equilibria. The model exhibits backward bifurcation generated by two mechanisms; standard incidence and superinfection. If the model does not allow for superinfection or deaths due to the disease, then DFE is globally stable which suggests that backward bifurcation is no longer possible. Simulations suggest that total prevalence of malaria is the highest if all individuals show symptoms upon infection, but then undergoes an incomplete treatment and the lowest when all the individuals first move to the symptomatic class then treated successfully. Total prevalence is average if more individuals upon infection move to the asymptomatic class. We study optimal control strategies applied to bed-net use and treatment as main tools for reducing the total number of symptomatic and asymptomatic individuals. Simulations suggest that the optimal control strategies are very dynamic. Although they always lead to decrease in the symptomatic infectious individuals, they may lead to increase in the number of asymptomatic infectious individuals. This last scenario occurs if a large portion of newly infected individuals move to the symptomatic class but many of them do not complete treatment or if they all complete treatment but the superinfection rate of asymptomatic individuals is average. [ABSTRACT FROM AUTHOR]

Human rabies was first recorded in ancient China in about 556 BC and is still one of the major public-health problems in China. From 1950 to 2015, 130,494 human rabies cases were reported in Mainland China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. The purpose of this article is to provide a review about the models, results, and simulations that we have obtained recently on studying the transmission of rabies in China. We first construct a basic susceptible, exposed, infectious, and recovered (SEIR) type model for the spread of rabies virus among dogs and from dogs to humans and use the model to simulate the human rabies data in China from 1996 to 2010. Then we modify the basic model by including both domestic and stray dogs and apply the model to simulate the human rabies data from Guangdong Province, China. To study the seasonality of rabies, in Section 4 we further propose a SEIR model with periodic transmission rates and employ the model to simulate the monthly data of human rabies cases reported by the Chinese Ministry of Health from January 2004 to December 2010. To understand the spatial spread of rabies, in Section 5 we add diffusion to the dog population in the basic SEIR model to obtain a reaction–diffusion equation model and determine the minimum wave speed connecting the disease-free equilibrium to the endemic equilibrium. Finally, in order to investigate how the movement of dogs affects the geographically inter-provincial spread of rabies in Mainland China, in Section 6 we propose a multi-patch model to describe the transmission dynamics of rabies between dogs and humans and use the two-patch submodel to investigate the rabies virus clades lineages and to simulate the human rabies data from Guizhou and Guangxi, Hebei and Fujian, and Sichuan and Shaanxi, respectively. Some discussions are provided in Section 7 . [ABSTRACT FROM AUTHOR]

The anthropophilic and peridomestic female mosquito Aedes aegypti bites humans to suck blood to maturate fertilized eggs, during which dengue virus can be spread between mosquito and human populations. Besides this route of transmission, there is a possibility of dengue virus being passed directly to offspring through transovarial (or vertical) transmission. The effects of both horizontal and transovarial transmission routes on the dengue virus transmission are assessed by mathematical modeling. From the model, the reproduction number is obtained and the contribution of transovarial transmission is evaluated for different levels of horizontal transmission. Notably, the transovarial transmission plays an important role in dengue spread when the reproduction number is near one. Another threshold parameter arises, which is the product of the fractions of the susceptible populations of humans and mosquitoes. Interestingly, these two threshold parameters can be obtained from three different approaches: the spectral radius of the next generation matrix, the Routh–Hurwitz criteria and M -matrix theory. [ABSTRACT FROM AUTHOR]

Dengue disease transmission is a complex vector-borne disease, mainly due to the co-circulation of four serotypes of the virus. Mathematical models have proved to be a useful tool to understand the complexity of this disease. In this work, we extend the model studied by Esteva et al., 2003, originally proposed for two serotypes, to four circulating serotypes. Using epidemic data of dengue fever in Iquitos (Peru) and San Juan (Puerto Rico), we estimate numerically the co-circulation parameter values for selected outbreaks using a bootstrap method, and we also obtained the Basic Reproduction Number, R 0 , for each serotype, using both analytical calculations and numerical simulations. Our results indicate that the impact of co-circulation of serotypes in population dynamics of dengue infection is such that there is a reduced effect from DENV-3 to DENV-4 in comparison to no-cross effect for epidemics in Iquitos. Concerning San Juan epidemics, also comparing to no-cross effect, we also observed a reduced effect from the predominant serotype DENV-3 to both DENV-2 and DENV-1 epidemics neglecting the very small number of cases of DENV-4. • The complex dynamics of vector-borne transmitted diseases, particularly Dengue, presents some features such us the co-circulation of serotypes. • The cross-reactivity between serotypes on an individual level may affect the dynamics of infection in population level. • We emphasize the relevance of Dengue's co-circulation of serotypes mainly for a safe tetravalent vaccine against dengue. • We present different scenarios confronting Dengue modeling and real epidemics data. • The study of nonlinear behavior of co-circulating variants is also relevant for other infectious diseases. [ABSTRACT FROM AUTHOR]

Japanese encephalitis (JE) is a public health problem that threats the entire world today. Japanese Encephalitis virus (JEV) mostly became a threat due to the significant number of increase of susceptible mosquito vectors and vertebrate hosts in Asia by which around 70,000 cases and 10,000 deaths per year took place in children below 15 years of age. In this paper, a mathematical model of JE due to JEV from the vector source (infected mosquito) and two vertebrate hosts (infected human and infected pig) is formulated. The disease can be controlled by applying several control measures such as vaccination, medicine and insecticide to the JE infection causing species. The model has been formulated as an optimal control problem and has been solved using Pontryagin’s maximum principle. Also, the stability of the system has been studied with the help of basic reproduction number for disease free and endemic equilibrium. The results of fixed control for endemic equilibrium is presented numerically and depicted graphically. The effects of different control strategies on human, pig and mosquito has been analyzed using Runge–Kutta 4th order forward and backward techniques and presented thereafter graphically. [ABSTRACT FROM AUTHOR]

The asymptotically homogeneous SIR model of Thieme (1992) for growing populations, with incidence depending in a general way on total population size, is reconsidered with respect to other parameterizations that give clear insight into epidemiological relevant relations and thresholds. One important feature of the present approach is case fatality as opposed to differential mortality. Although case fatality models and differential mortality models are equivalent via a transformation in parameter space, the underlying ideas and the dynamic behaviors are different, e.g. the basic reproduction number depends on differential mortality but not on case fatality. The persistent distributions and exponents of growth of infected solutions are computed and discussed in terms of the parameters. The notion of asymptotically exponentially growing state (as opposed to stationary state or exponential solution) coined by Thieme is interpreted in terms of stability theory. Of some interest are limiting cases of models without recovery where two infected solutions exist. [ABSTRACT FROM AUTHOR]

A novel alcoholism model which involves impact of Twitter is formulated. It is shown that the model has multiple equilibria. Stability of all the equilibria are obtained in terms of the basic reproductive number R 0 . Using the center manifold theory, the occurrence of backward and forward bifurcation for a certain defined range of R 0 are established. Furthermore, the existence of Hopf bifurcation is also established by regarding the transmission coefficient β as the bifurcation parameter. Numerical simulations and sensitivity analysis on a few parameters are also carried out. Our results show that Twitter can serve as a good indicator of alcoholism model and affect the spread of the drinking. [ABSTRACT FROM AUTHOR]

A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts’ dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R 0 is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if R 0 ≤ 1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R 0 > 1 whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness , a measure of host-vector heterogeneous structure, on the basic reproduction number R 0 , are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence. [ABSTRACT FROM AUTHOR]

While studies on pre-exposure prophylaxis (PrEP) and post-exposure prophylaxis (PEP) have demonstrated substantial advantages in controlling HIV transmission, the overall benefits of the programs with early initiation of antiretroviral therapy (ART) have not been fully understood and are still on debate. Here, we develop an immunity-based (CD4+ T cell count based) mathematical model to study the impacts of early treatment programs on HIV epidemics and the overall community-level immunity. The model is parametrized using the HIV prevalence data from South Africa and fully analyzed for stability of equilibria and infection persistence criteria. Using our model, we evaluate the effects of early treatment on the new infection transmission, disease death, basic reproduction number, HIV prevalence, and the community-level immunity. Our model predicts that the programs with early treatments significantly reduce the new infection transmission and increase the community-level immunity, but the treatments alone may not be enough to eliminate HIV epidemics. These findings, including the community-level immunity, might provide helpful information for proper implementation of HIV treatment programs. [ABSTRACT FROM AUTHOR]

We consider the dynamics of a mosquito-transmitted pathogen in a multi-patch Ross–Macdonald malaria model with mobile human hosts, mobile vectors, and a heterogeneous environment. We show the existence of a globally stable steady state, and a threshold that determines whether a pathogen is either absent from all patches, or endemic and present at some level in all patches. Each patch is characterized by a local basic reproduction number, whose value predicts whether the disease is cleared or not when the patch is isolated: patches are known as “demographic sinks” if they have a local basic reproduction number less than one, and hence would clear the disease if isolated; patches with a basic reproduction number above one would sustain endemic infection in isolation, and become “demographic sources” of parasites when connected to other patches. Sources are also considered focal areas of transmission for the larger landscape, as they export excess parasites to other areas and can sustain parasite populations. We show how to determine the various basic reproduction numbers from steady state estimates in the patched network and knowledge of additional model parameters, hereby identifying parasite sources in the process. This is useful in the context of control of the infection on natural landscapes, because a commonly suggested strategy is to target focal areas, in order to make their corresponding basic reproduction numbers less than one, effectively turning them into sinks. We show that this is indeed a successful control strategy—albeit a conservative and possibly expensive one—in case either the human host, or the vector does not move. However, we also show that when both humans and vectors move, this strategy may fail, depending on the specific movement patterns exhibited by hosts and vectors. [ABSTRACT FROM AUTHOR]

Symptom severity affects disease transmission both by impacting contact rates, as well as by influencing the probability of transmission given contact. This involves a trade-off between these two factors, as increased symptom severity will tend to decrease contact rates, but increase the probability of transmission given contact (as pathogen shedding rates increase with symptom severity). This paper explores this trade-off between contact and transmission given contact, using a simple compartmental susceptible-infected-recovered type model. Under mild assumptions on how contact and transmission probability vary with symptom severity, we give sufficient, biologically intuitive criteria for when the basic reproduction number varies non-monotonically with symptom severity. Multiple critical points are possible. We give a complete characterization of the region in parameter space where multiple critical points are located in the special case where contact rate decreases exponentially with symptom severity. We consider a multi-strain version of the model with complete cross-immunity and no super-infection. In this model, we prove that the strain with highest basic reproduction number drives the other strains to extinction. This has both evolutionary and epidemiological implications, including the possibility of an intervention paradoxically resulting in increased infection prevalence. [ABSTRACT FROM AUTHOR]

In this paper we consider epidemic models of directly transmissible SIR (susceptible → infective → recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting either of households or of households and workplaces. We review most reproduction numbers defined in the literature for these models, including the basic reproduction number R 0 introduced in the companion paper of this, for which we provide a simpler, more elegant derivation. Extending previous work, we provide a complete overview of the inequalities among these reproduction numbers and resolve some open questions. Special focus is put on the exponential-growth-associated reproduction number R r , which is loosely defined as the estimate of R 0 based on the observed exponential growth of an emerging epidemic obtained when the social structure is ignored. We show that for the vast majority of the models considered in the literature R r ≥ R 0 when R 0 ≥ 1 and R r ≤ R 0 when R 0 ≤ 1. We show that, in contrast to models without social structure, vaccination of a fraction 1 − 1 / R 0 of the population, chosen uniformly at random, with a perfect vaccine is usually insufficient to prevent large epidemics. In addition, we provide significantly sharper bounds than the existing ones for bracketing the critical vaccination coverage between two analytically tractable quantities, which we illustrate by means of extensive numerical examples. [ABSTRACT FROM AUTHOR]

In this work, we investigate the spread and control of sexually transmitted diseases when a game-theory based vaccination strategy is involved. An individual’s decision on vaccination uptake may follow a cost-benefit analysis since the individual obtains immunity against the disease from the vaccination and, at the same time, may have some perceived side effects. Evolutionary game theory is integrated into the epidemic model to reveal the relationship between individuals’ voluntary decisions on vaccination uptake and the spread and control of such diseases. We show that decreasing the perceived cost of taking vaccine or increasing the payoff from social obligation is beneficial to controlling the disease. It is also shown how the “degree of rationality” of males and females affects the disease spread through the net payoff of the game. In particular, individual awareness of the consequences of the disease on the infectives also contributes to slowing down the disease spread. By analyzing an asymmetric version of our evolutionary game, it is shown that the disease is better controlled when individuals are more sensitive to fitness differences when net payoff is positive than when it is negative. [ABSTRACT FROM AUTHOR]