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Hosts can activate a defensive response to clear the parasite once being infected. To explore how host survival and fecundity are affected by host-parasite coevolution for chronic parasitic diseases, in this paper, we proposed an age-structured epidemic model with infection age, in which the parasite transmission rate and parasite-induced mortality rate are structured by the infection age. By use of critical function analysis method, we obtained the existence of the host immune evolutionary singular strategy which is a continuous singular strategy (CSS). Assume that parasite-induced mortality begins at infection age τ and is constant v thereafter. We got that the value of the CSS, c ∗ , monotonically decreases with respect to infection age τ (see Case (I)), while it is non-monotone if the constant v positively depends on the immune trait c (see Case (II)). This non-monotonicity is verified by numerical simulations and implies that the direction of immune evolution depends on the initial value of immune trait. Besides that, we adopted two special forms of the parasite transmission rate to study the parasite’s virulence evolution, by maximizing the basic reproduction ratio R 0 . The values of the convergence stable parasite’s virulence evolutionary singular strategies v ∗ and k ∗ increase monotonically with respect to time lag L (i.e., the time lag between the onset of transmission and mortality). At the singular strategy v ∗ and k ∗ , we further obtained the expressions of the case mortalities χ ∗ and how they are affected by the time lag L. Finally, we only presented some preliminary results about host and parasite coevolution dynamics, including a general condition under which the coevolutionary singular strategy (c ∗ , v ∗) is evolutionarily stable. [ABSTRACT FROM AUTHOR]

Syphilis and HIV infections form a dangerous combination. In this paper, we propose an epidemic model of HIV-syphilis coinfection. The model always has a unique disease-free equilibrium, which is stable when both reproduction numbers of syphilis and HIV are less than 1. If the reproduction number of syphilis (HIV) is greater than 1, there exists a unique boundary equilibrium of syphilis (HIV), which is locally stable if the invasion number of HIV (syphilis) is less than 1. Coexistence equilibrium exists and is stable when all reproduction numbers and invasion numbers are greater than 1. Using data of syphilis cases and HIV cases from the US, we estimated that both reproduction numbers for syphilis and HIV are slightly greater than 1, and the boundary equilibrium of syphilis is stable. In addition, we observed competition between the two diseases. Treatment for primary syphilis is more important in mitigating the transmission of syphilis. However, it might lead to increase of HIV cases. The results derived here could be adapted to other multi-disease scenarios in other regions. [ABSTRACT FROM AUTHOR]

Seagrass meadows always provide a habitat for many kinds of fish. As the environment changes, some kinds of fish persist if they can evolve a positive growth rate to avoid extinction and others go to extinct in the habitat. To reveal the roles of environment and ability to evolve on the predator population persistence, in this paper, we formulate an age structured model by adopting the seagrass residence index (SRI) as the environment variable. By uniform persistence and stability analysis, we obtain the detailed dynamic behaviors of the age structured model which are mainly determined by the two thresholds η 1 ∗ and η 2 ∗ for the conversion rate η . If η < η 1 ∗ , the density of the predator population will go to zero. If η > η 1 ∗ , there is a unique positive steady state E ∗ and the predator population will be uniformly persistent. If η 1 ∗ < η < η 2 ∗ , the unique positive steady state E ∗ is stable and the predator population can establish itself in the environment. If η > η 2 ∗ , the unique positive steady state E ∗ will lose its stability and Hopf bifurcation occurs when maturation age τ = 0 . If τ > 0 , maturation age τ will play a key role in the stability criteria for the positive steady state E ∗ , and the establishment of the predator population will become more difficult and complex. Numerical simulations are presented to verify the theoretical results and reveal the evolution of predator population adaptation to the habitat. [ABSTRACT FROM AUTHOR]

Human papillomavirus (HPV) infection can spread between regions. What is the impact of disassortative geographical mixing on the dynamics of HPV transmission? Vaccination is effective in preventing HPV infection. How to allocate HPV vaccines between genders within each region and between regions to reduce the total infection? Here we develop a two-patch two-sex model to address these questions. The control reproduction number R 0 under vaccination is obtained and shown to provide a critical threshold for disease elimination. Both analytical and numerical results reveal that disassortative geographical mixing does not affect R 0 and only has a minor impact on the disease prevalence in the total population given the vaccine uptake proportional to the population size for each gender in the two patches. When the vaccine uptake is not proportional to the population size, sexual mixing between the two patches can reduce R 0 and mitigate the consequence of disproportionate vaccine coverage. Using parameters calibrated from the data of a case study, we find that if the two patches have the same or similar sex ratios, allocating vaccines proportionally according to the new recruits in two patches and giving priority to the gender with a smaller recruit rate within each patch will bring the maximum benefit in reducing the total prevalence. We also show that a time-variable vaccination strategy between the two patches can further reduce the disease prevalence. This study provides some quantitative information that may help to develop vaccine distribution strategies in multiple regions with disassortative mixing. [ABSTRACT FROM AUTHOR]

In ecological systems, the fear of predation risk may assert privilege to the prey species by restricting their exposure to potential predators, and also impose costs by constraining the exploration of optimal resources. In this paper, an eco-epidemic model of the predator–prey system is investigated by considering disease in prey population and selective behavior of predator; the cost of fear is taken as affecting the reproduction and intraspecies competition of vulnerable prey population, and also lowers the disease transmission; the predators are assumed to cooperate with each other for the hunting while the susceptible/infected prey population takes refuge. Numerical observations of the system demonstrate that the cost of fear causing a reduction in the birth rate of susceptible prey has a destabilizing role, whereas the levels of fear responsible for the increase in the intraspecies competition of susceptible prey and eradication of the disease prevalence have the capacity to stabilize an otherwise unstable system. The intensity of disease prevalence potentially affects the dynamics of the ecosystem by altering its stability around the infection-free state and the coexistence of prey and predator species. However, refuge taken by the susceptible/infected prey has the potential to restore the stability of the system. Moreover, the chaotic nature of the system is observed if the preference of predators for susceptible prey or hunting cooperation of predators exceeds a fixed value. We also investigate the dynamics of the system by letting some of the model parameters to vary with time. Our numerical results for the seasonally forced system showcase different dynamical features including periodic solutions, higher periodic solutions, bursting patterns, and chaos. [ABSTRACT FROM AUTHOR]

In this paper, a two-strain model with coinfection that links immunological and epidemiological dynamics across scales is formulated. On the with-in host scale, the two strains eliminate each other with the strain having the larger immunological reproduction number persisting. However, on the population scale coinfection is a common occurrence. Individuals infected with strain one can become coinfected with strain two and similarly for individuals originally infected with strain two. The immunological reproduction numbers R j , the epidemiological reproduction numbers R j and invasion reproduction numbers R j i are computed. Besides the disease-free equilibrium, there are strain one and strain two dominance equilibria. The disease-free equilibrium is locally asymptotically stable when the epidemiological reproduction numbers R j are smaller than one. In addition, each strain dominance equilibrium is locally asymptotically stable if the corresponding epidemiological reproduction number is larger than one and the invasion reproduction number of the other strain is smaller than one. The coexistence equilibrium exists when all the reproduction numbers are greater than one. Simulations suggest that when both invasion reproduction numbers are smaller than one, bistability occurs with one of the strains persisting or the other, depending on initial conditions. [ABSTRACT FROM AUTHOR]

The ongoing COVID-19 pandemic has affected most of the countries on Earth. It has become a pandemic outbreak with more than 50 million confirmed infections and above 1 million deaths worldwide. In this study, we consider a mathematical model on COVID-19 transmission with the prosocial awareness effect. The proposed model can have four equilibrium states based on different parametric conditions. The local and global stability conditions for awareness-free, disease-free equilibrium are studied. Using Lyapunov function theory and LaSalle invariance principle, the disease-free equilibrium is shown globally asymptotically stable under some parametric constraints. The existence of unique awareness-free, endemic equilibrium and unique endemic equilibrium is presented. We calibrate our proposed model parameters to fit daily cases and deaths from Colombia and India. Sensitivity analysis indicates that the transmission rate and the learning factor related to awareness of susceptibles are very crucial for reduction in disease-related deaths. Finally, we assess the impact of prosocial awareness during the outbreak and compare this strategy with popular control measures. Results indicate that prosocial awareness has competitive potential to flatten the COVID-19 prevalence curve. [ABSTRACT FROM AUTHOR]

In this paper we formulate a multi-scale nested immuno-epidemiological model of HIV on complex networks. The system is described by ordinary differential equations coupled with a partial differential equation. First, we prove the existence and uniqueness of the immunological model and then establish the well-posedness of the multi-scale model. We derive an explicit expression of the basic reproduction number R 0 of the immuno-epidemiological model. The system has a disease-free equilibrium and an endemic equilibrium. The disease-free equilibrium is globally stable when R 0 < 1 and unstable when R 0 > 1 . Numerical simulations suggest that R 0 increases as the number of nodes in the network increases. Further, we find that for a scale-free network the number of infected individuals at equilibrium is a hump-like function of the within-host reproduction number; however, the dependence becomes monotone if the network has predominantly low connectivity nodes or high connectivity nodes. [ABSTRACT FROM AUTHOR]

Vaccination is effective in preventing human papillomavirus (HPV) infection. It is imperative to investigate who should be vaccinated and what the best vaccine distribution strategy is. In this paper, we use a dynamic model to assess HPV vaccination strategies in a heterosexual population combined with gay, bisexual, and other men who have sex with men (MSM). The basic reproduction numbers for heterosexual females, heterosexual males and MSM as well as their average for the total population are obtained. We also derive a threshold parameter, based on basic reproduction numbers, for model analysis. From the analysis and numerical investigations, we have several conclusions. (1) To eliminate HPV infection, the priority of vaccination should be given to MSM, especially in countries that have already achieved high coverage in females. The heterosexual population gets great benefit but MSM only get minor benefit from vaccinating heterosexual females or males. (2) The best vaccination strategy is to vaccinate MSM firstly as many as possible, then heterosexual females, lastly heterosexual males. (3) Given a fixed vaccination coverage of MSM, distributing the remaining vaccines to only heterosexual females or males leads to a similar prevalence in the total population. This prevalence is lower than that when vaccines are distributed to both genders. The evener the distribution, the higher the prevalence in the total population. (4) Vaccination becomes less effective in reducing the prevalence as more vaccines are given. It is more effective to allocate vaccines to a region with lower vaccination coverage. This study provides information that may help policymakers formulate guidelines for vaccine distribution to reduce HPV prevalence on the basis of vaccine availability and prior vaccination coverage. Whether these guidelines are affected when the objective is to reduce HPV-associated cancer incidence remains to be further studied. [ABSTRACT FROM AUTHOR]

Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host's immune system influences the pathogen's transmission potential between hosts via vectors. Yet there are few theoretical studies on virulence-transmission trade-offs and evolution in vector-borne pathogen-host systems. Here, we consider an immuno-epidemiological model that links the within-host dynamics to between-host circulation of a vector-borne disease. On the immunological scale, the model mimics antibody-pathogen dynamics for arbovirus diseases, such as Rift Valley fever and West Nile virus. The within-host dynamics govern transmission and host mortality and recovery in an age-since-infection structured host-vector-borne pathogen epidemic model. By considering multiple pathogen strains and multiple competing host populations differing in their within-host replication rate and immune response parameters, respectively, we derive evolutionary optimization principles for both pathogen and host. Invasion analysis shows that the $${\mathcal {R}}_0$$ maximization principle holds for the vector-borne pathogen. For the host, we prove that evolution favors minimizing case fatality ratio (CFR). These results are utilized to compute host and pathogen evolutionary trajectories and to determine how model parameters affect evolution outcomes. We find that increasing the vector inoculum size increases the pathogen $${\mathcal {R}}_0$$ , but can either increase or decrease the pathogen virulence (the host CFR), suggesting that vector inoculum size can contribute to virulence of vector-borne diseases in distinct ways. [ABSTRACT FROM AUTHOR]

In this article, we discuss the structural and practical identifiability of a nested immuno-epidemiological model of arbovirus diseases, where host-vector transmission rate, host recovery, and disease-induced death rates are governed by the within-host immune system. We incorporate the newest ideas and the most up-to-date features of numerical methods to fit multi-scale models to multi-scale data. For an immunological model, we use Rift Valley Fever Virus (RVFV) time-series data obtained from livestock under laboratory experiments, and for an epidemiological model we incorporate a human compartment to the nested model and use the number of human RVFV cases reported by the CDC during the 2006-2007 Kenya outbreak. We show that the immunological model is not structurally identifiable for the measurements of time-series viremia concentrations in the host. Thus, we study the non-dimensionalized and scaled versions of the immunological model and prove that both are structurally globally identifiable. After fixing estimated parameter values for the immunological model derived from the scaled model, we develop a numerical method to fit observable RVFV epidemiological data to the nested model for the remaining parameter values of the multi-scale system. For the given (CDC) data set, Monte Carlo simulations indicate that only three parameters of the epidemiological model are practically identifiable when the immune model parameters are fixed. Alternatively, we fit the multi-scale data to the multi-scale model simultaneously. Monte Carlo simulations for the simultaneous fitting suggest that the parameters of the immunological model and the parameters of the immuno-epidemiological model are practically identifiable. We suggest that analytic approaches for studying the structural identifiability of nested models are a necessity, so that identifiable parameter combinations can be derived to reparameterize the nested model to obtain an identifiable one. This is a crucial step in developing multi-scale models which explain multi-scale data. [ABSTRACT FROM AUTHOR]

This paper considers global asymptotic properties for an age-structured model of heroin use based on the principles of mathematical epidemiology where the incidence rate depends on the age of susceptible individuals. The basic reproduction number of the heroin spread is obtained. It completely determines the stability of equilibria. By using the direct Lyapunov method with Volterra type Lyapunov function, the authors show that the drug-free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and the unique drug spread equilibrium is globally asymptotically stable if the basic reproduction number is greater than one. [ABSTRACT FROM AUTHOR]

We introduce a model of avian influenza in domestic birds with imperfect vaccination and age-since-vaccination structure. The model has four components: susceptible birds, vaccinated birds (stratified by vaccination age), asymptomatically infected birds, and infected birds. The model includes reduction in the probability of infection, decreasing severity of disease of vaccinated birds and vaccine waning. The basic reproduction number, $$\mathcal R_0$$ , is calculated. The disease-free equilibrium is found to be globally stable under certain conditions when $${\mathcal {R}}_0<1$$ . When $${\mathcal {R}}_0>1$$ , existence of an endemic equilibrium is proved (with uniqueness for the ODE case and local stability under stricter conditions) and uniform persistence of the disease is established. The inclusion of reduction in susceptibility of vaccinated birds, reduction in infectiousness of asymptomatically infected birds and vaccine waning can have important implications for disease control. We analytically and numerically demonstrate that vaccination can paradoxically increase the total number of infected, resulting in the 'silent spread' of the disease. We also study the effects of vaccine efficacy on disease prevalence and the minimum critical vaccination coverage, a threshold value for vaccination coverage to avoid an increase in total disease prevalence due to asymptomatic infection. [ABSTRACT FROM AUTHOR]

This article investigates the impact of predation on the coexistence and competitive exclusion of pathogen strains in the prey. Two types of predator are considered- a generalist and a specialist. For each type of predator, we assume that the predator can discriminate among susceptible and infected with each strain prey. The two strains will competitively exclude each other in the absence of predation with the strain with the larger reproduction number persisting. If a generalist predator preys discriminantly and the disease is fatal, then depending on the predation level, a switch in the dominant pathogen may occur. Thus, for some predation levels, the first strain may persist while for other predation levels the second strain may persist. Furthermore, a specialist predator preying discriminantly may mediate the coexistence of the two strains. Although in most cases increasing predation reduces the disease load in the prey, when predation leads to coexistence, it may also lead to increase in the disease load. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Levins-type metapopulation model with empty and occupied patches, and dispersing population. We structure the proportion of occupied patches according to the patch-occupancy age. We observe that patch-occupancy age may destabilize the metapopulation, leading to persistent oscillations. We also allow for the dispersal rate to vary with the proportion of empty patches in a monotone or unimodal way. The unimodal dependence leads to multiple non-trivial equilibria and bistability when the reproduction number of the metapopulation R < 1 but greater than a lower critical value R*. We show that the metapopulation will persist independently of its initial status if R > 1. [ABSTRACT FROM AUTHOR]