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In the current study, we present a mathematical model for human immunodeficiency virus type-1 (HIV -1) transmission, incorporating Cytotoxic T-Lymphocyte immune impairment within a seasonal environment. The model divides the infected cell compartment into two sub-compartments: latently infected cells and productively infected cells. Additionally, we consider three possible routes of infection, allowing HIV to spread among susceptible cells via direct contact with the virus, latently infected cells, or productively infected cells. The system is analyzed, and the basic reproduction number is derived using an integral operator. We demonstrate that the HIV -free periodic trajectory is globally asymptotically stable if R 0 < 1 , while HIV persists when R 0 > 1. Several numerical simulations are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we proposed and studied a simple five-dimensional mathematical model that describes the second and third stages of the anaerobic degradation process under the influence of leachate recirculation. The state variables are the concentration of insoluble substrate, soluble substrate, produced hydrogen, acetogenic bacteria and hydrogenotrophic-methanogenic bacteria. The growth rates of used bacteria will be of general nonlinear form. The stability of the steady states will be studied by reducing the model to a 3D system. According to the operating parameters of the bioreactor described by the added insoluble substrate, soluble substrate and hydrogen input concentrations and the dilution rate, we proved that the model can admit multiple equilibrium points and we gave the necessary and sufficient assumptions for their existence, their uniqueness and their stability. In particular, the uniform persistence of the system was satisfied under some natural assumptions on the growth rates. Then, a question was answered related to the management of renewable resources where the goal of was to propose an optimal strategy of leachate recirculation to reduce the organic matter (either soluble or insoluble) and keep a limitation of the costs of the recirculation operation during the process. The findings of this work were validated by an intensive numerical investigation. [ABSTRACT FROM AUTHOR]

Past works on partially diffusive models of diseases typically rely on a strong assumption regarding the initial data of their infection-related compartments in order to demonstrate uniform persistence in the case that the basic reproduction number R 0 is above 1. Such a model for avian influenza was proposed, and its uniform persistence was proven for the case R 0 > 1 when all of the infected bird population, recovered bird population and virus concentration in water do not initially vanish. Similarly, a work regarding a model of the Ebola virus disease required that the infected human population does not initially vanish to show an analogous result. We introduce a modification on the standard method of proving uniform persistence, extending both of these results by weakening their respective assumptions to requiring that only one (rather than all) infection-related compartment is initially non-vanishing. That is, we show that, given R 0 > 1 , if either the infected bird population or the viral concentration are initially nonzero anywhere in the case of avian influenza, or if any of the infected human population, viral concentration or population of deceased individuals who are under care are initially nonzero anywhere in the case of the Ebola virus disease, then their respective models predict uniform persistence. The difficulty which we overcome here is the lack of diffusion, and hence the inability to apply the minimum principle, in the equations of the avian influenza virus concentration in water and of the population of the individuals deceased due to the Ebola virus disease who are still in the process of caring. [ABSTRACT FROM AUTHOR]

We derive a mathematical model that describes the competition of two populations in a chemostat in the presence of a virus. We suppose that only one population is affected by the virus. We also suppose that the substrate is continuously added to the bioreactor. We obtain a model taking the form of an "SI" epidemic model using general increasing growth rates of bacteria on the substrate and a general increasing incidence rate for the viral infection. The stability of the steady states was carried out. The system can have multiple steady states with which we can determine the necessary and sufficient conditions for both existence and local stability. We exclude the possibility of periodic orbits and we prove the uniform persistence of both species. Finally, we give some numerical simulations that validate the obtained results. [ABSTRACT FROM AUTHOR]

For a hepatitis C virus (HCV) mathematical model considering host immune system which is studied by Blé et al. (2018), uniform persistence and global asymptotic stability of the endemic equilibrium of the model are considered, and a set of feasible sufficient conditions are obtained by constructing appropriate Lyapunov functions. Our results largely improved those in related works. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a detailed mathematical model describing the dynamics of a prey-predator model under the influence of an SIS infectious disease by using nonlinear differential equations. We use the functional response of ratio-dependent Michaelis-Menten type to describe the predation strategy. In the presence of the disease, prey and predator population are divided into two disjointed classes, namely infected and susceptible. The first one is governed through due predation interaction, and the second one is governed through the propagation of disease in the prey and predator population via predation. Our aim is to analyze the effect of predation on the dynamic of the disease transmission. Important mathematical results resulting from the transmission of the disease under influence of predation are offered. First, results concerning boundedness, uniform persistence, existence and uniqueness of solutions have been developed. In addition, many thresholds have been computed and used to investigate local and global stability analysis by using Routh-Hurwitz criterion and Lyapunov principle. We also establish the Hopf bifurcation to highlight periodic fluctuation with persistence of the disease or without disease in the prey and predator population. Finally, numerical simulations are carried out to illustrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we consider a 4-dimensional predator–prey chemostat model of nitrogen-phytoplankton-rotifer interactions with staged structure proposed by Blasius et al. (2020). Although it is still difficult to prove the simulation observations in Blasius et al. (2020) by mathematical arguments, we explore the dynamics in order to better understand the dynamical mechanism of cyclic persistence for this model. We firstly investigate the corresponding system without staged structure, i.e., when the juvenile is absent, the asymptotical behavior of the solutions is given. When the juvenile is present, a threshold condition for the uniform persistence of the 4-dimensional system is provided. Finally, by choosing the life development time delay as a bifurcation parameter, we show that the system admits periodic solutions near one semi-equilibrium undergoing Hopf bifurcation. The rigorous theoretical analytic work in this paper provides some helpful transient information between coherent oscillation and non-coherent oscillation described by the experimental data of Blasius et al. (2020). [ABSTRACT FROM AUTHOR]

The goal of this paper is to explain how to derive the classical Rosenzweig--MacArthur model by using a model with two groups of predators in which we can separate the vital dynamic and consumption of prey to describe the behavior of the predators. This will be especially very convenient if we want to add an age or size structure to the predator population. As mentioned by Holling (without mathematical model), we divide the population of predators into the searching and the handling predators. In this article we study some properties of this model and conclude by proving that the model converges to the classical Rosenzweig--MacArthur model by using an appropriate rescaling. This convergence property is observed by using numerical simulations. We also apply this model to the Canadian snowshoe hares and the lynx. [ABSTRACT FROM AUTHOR]

In this paper, we develop and analyze a malaria model with seasonality of mosquito life‐history traits: periodic‐mosquitoes per capita birth rate, ‐mosquitoes death rate, ‐probability of mosquito to human disease transmission, ‐probability of human to mosquito disease transmission, and ‐mosquitoes biting rate. All these parameters are assumed to be time dependent leading to a nonautonomous differential equation system. We provide a global analysis of the model depending on two threshold parameters R0 and R¯0<1 (with R0≤R¯0). When R0<1, then the disease‐free stationary state is locally asymptotically stable. In the presence of the human disease‐induced mortality, the global stability of the disease‐free stationary state is guarantied when R¯0<1. On the contrary, if R0>1, the disease persists in the host population in the long term and the model admits at least one positive periodic solution. Moreover, by a numerical simulation, we show that a sub‐critical (backward) bifurcation is possible at R0=1. Finally, the simulation results are in accordance with the seasonal variation of the reported cases of a malaria‐epidemic region in Mpumalanga province in South Africa. [ABSTRACT FROM AUTHOR]

In this paper we focus on a patch occupancy 4-dimensional model of barnacle-algae-mussel interactions with external periodic seasonal forcing proposed by Benincà et al. [Proc. Natl. Acad. Sci. USA, 112 (2015), pp. 6389--6394]. In order to understand the mechanism of the species fluctuation sustained by a cyclic succession at the edge of chaos, we investigate the corresponding system without seasonal forcing. When the mussel is absent, we give a complete description of the global asymptotic behavior of the solutions. If the mussel is present, we provide an amenable sufficient and necessary condition for the uniform persistence for the 4-dimensional system. Our analytic results on the uniform persistence provide useful necessary information for the chaotic dynamics of the periodically forced system Benincà et al. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a nonautonomous and an autonomous model of schistosomiasis transmission with a general incidence function. Firstly, we formulate the nonautonomous model by taking into account the effect of climate change on the transmission. Through rigorous analysis via theories and methods of dynamical systems, we show that the nonautonomous model has a globally asymptotically stable disease-free periodic equilibrium when the associated basic reproduction ratio ℛ 0 is less than unity. Otherwise, the system admits at least one positive periodic solutions if ℛ 0 is greater than unity. Secondly, using the average of periodic functions, we further derive the autonomous model associated with the nonautonomous model. Therefore, we show that the disease-free equilibrium of the autonomous model is locally and globally asymptotically stable when the associated reproduction ratio ℛ 1 is less than unity. When ℛ 1 is greater than unity, the existence and global asymptotic stability of the endemic equilibrium is established under certain conditions. Finally, using linear and nonlinear specific incidence function, we perform some numerical simulations to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey-predator interactions. Of primary interests are the underlying structure and features which stabilize diverse ecological networks. Recently Korytowski and Smith (Theor Ecol 8(1):111-120, 2015) proved that a perfectly nested infection network, along with appropriate life history trade-offs, leads to coexistence and persistence of bacteria-phage communities in a chemostat model. In this article, we generalize their model in order to apply it to the within-host dynamics virus and immune response, in particular HIV and CTL (Cytotoxic T Lymphocyte) cells. Our model can describe sequential viral escape from dominant immune responses and rise in subdominant immune responses, consistent with observed patterns of HIV/CTL evolution. We find a Lyapunov function for the system which leads to rigorous characterization of persistent viral and immune variants, along with informing upon equilibria stability and global dynamics. Results are interpreted in the context of within-host HIV/CTL evolution and numerical simulations are provided. [ABSTRACT FROM AUTHOR]

We investigate a discrete consumer-resource system based on a model originally proposed for studying the cyclic dynamics of the larch budmoth population in the Swiss Alps. It is shown that the moth population can persist indefinitely for all of the biologically feasible parameter values. Using intrinsic growth rate of the consumer population as a bifurcation parameter, we prove that the system can either undergo a period-doubling or a Neimark–Sacker bifurcation when the unique interior steady state loses its stability. [ABSTRACT FROM AUTHOR]

With the consideration of the mechanism of prevention and control for the spread of dengue fever, a mathematical model of dengue fever dynamical transmission between mosquitoes and humans, incorporating a vector control strategy of impulsive culling of mosquitoes, is proposed in this paper. By using the comparison principle, Floquet theory and some of analytical methods, we obtain the basic reproductive number R0 for this infectious disease, which illustrates the stability of the disease-free periodic solution and the uniform persistence of the disease. Further, the explicit conditions determining the backward or forward bifurcation are obtained and we show that the culling rate ϕ has a major effect on the occurrence of backward bifurcation. Finally, numerical simulations are given to verify the correctness of theoretical results and the highest efficiency of vector control strategy. [ABSTRACT FROM AUTHOR]

In this paper we propose a prey-predator model in multiple patches through the stage structured maturation time delay with migrations among patches. Focus on the case with two patches, we discuss the existence of equilibrium points and the uniform persistence. In particular, when the maturation times are the same in the patches, we study the local and global attractivity of boundary equilibrium point with general migration function and the local stability of the positive equilibrium with constant migration rate. Numerical simulations are provided to demonstrate the theoretical results, to illustrate the effect of the maturation time, the migration rate on the dynamical behavior of the system. [ABSTRACT FROM AUTHOR]

SIR infection age models with a very general class of nonlinear incidence rates f ( S , J ) are investigated. We give a necessary and sufficient condition for global asymptotic stability of the free-equilibrium related to the basic reproduction number. Furthermore, additional conditions allow us to prove an exponential stability of this disease-free equilibrium. Finally, by using a Lyapunov functional, we show the global asymptotic stability of the endemic equilibrium whenever it exists. [ABSTRACT FROM AUTHOR]

Hand-foot-mouth disease (HFMD) has spread widely in mainland China increasing in prevalence in most years with serious consequences for child health. The HFMD virus can survive for a long period outside the host in suitable conditions, and hence contaminated environments may play important roles in HFMD infection. A new mathematical model was proposed and used to investigate the roles that asymptomatic individuals and contaminated environments played in HFMD dynamics. The model includes both direct transmission between susceptible and infected individuals and indirect transmission via free-living infectious unites in the environment. Theoretical analysis shows that the disease goes to extinction if the basic reproduction number is less than unity, whilst otherwise the disease persists. By fitting the proposed model to surveillance data we estimated the basic reproduction number as 1.509. Numerical simulations show that increasing the rate of virus clearance and decreasing transmission rates can delay epidemic outbreaks and weaken the severity of HFMD. Sensitivity analysis indicated that the basic reproduction number is sensitive to the transmission rate induced by asymptomatic infectious individuals and parameters associated with contaminated environments such as the indirect transmission rate, the rate of clearance and the virus shedding rates. This implies that asymptomatic infectious individuals and contaminated environments contribute substantially to new HFMD infections, and so would be targets for effective control measures. [ABSTRACT FROM AUTHOR]

This paper studies an eigenvalue problem associated with a linear parabolic equation and a coupled ordinary differential equation. The existence and the uniqueness of the principal eigenvalue for this eigenvalue problem is first established. Then, the qualitative dependence of the principal eigenvalue with respect to the several parameters involved in the system is analyzed. Finally, these results are applied to a system in flowing habitats with a hydraulic storage zone and light limitation. [ABSTRACT FROM AUTHOR]

In this work, we consider a three species Lotka–Volterra food web model with omnivory which is defined as feeding on more than one trophic level. Based on a non-dimensional transformation, the model actually becomes a system of three first order ordinary differential equations with seven parameters. Analytically, we completely classify the parameter space into three categories containing eight cases, show the extinction results for five cases, and verify uniform persistence for the other three cases. Moreover, in the region of the parameter space where the system is uniformly persistent we prove the existence of periodic solutions via Hopf bifurcation and present the chaotic dynamics numerically. Biologically, the omnivory module blends the attributes of several well-studied community modules, such as food chains (food chain models), exploitative competition (two predators–one prey models), and apparent competition (one predator–two preys models). We try to point out the differences and similarities among these models quantitatively and give the biological interpretations. [ABSTRACT FROM AUTHOR]

We consider a model of the exploitative competition of two micro-organisms for two complementary nutrients in a chemostat and take into account the interspecific interaction. The growth functions occurring in the model are of general type and the interaction functions are monotonic and positive. By the mean of the Thieme-Zhao theorem, we establish conditions for uniform persistence of the model. [ABSTRACT FROM AUTHOR]

To study the effect of immune response in viral infections, a new mathematical model is proposed and analyzed. It describes the interactions between susceptible host cells, infected host cells, free virus, lytic and nonlytic immune response. Using the LaSalle's invariance principle, we establish conditions for the global stability of equilibria. Uniform persistence is obtained when there is a unique endemic equilibrium. Mathematical analysis and numerical simulations indicate that the basic reproduction number of the virus and immune response reproductive number are sharp threshold parameters to determine outcomes of infection. Lytic and nonlytic antiviral activities play a significant role in the amount of susceptible host cells and immune cells in the endemic steady state. We also present potential applications of the model in clinical practice by introducing antiviral effects of antiviral drugs. [ABSTRACT FROM AUTHOR]

In this paper, by utilizing the comparison theorem and constructing a suitable Lyapunov functional the predator-prey model with modified Leslie-Gower Holling-type II schemes and a deviating argument is studied. Some sufficient conditions are obtained for uniform persistence and global attractivity of positive periodic solutions for this model. Furthermore, an example shows that the obtained criteria are easily verifiable. [ABSTRACT FROM AUTHOR]

This paper is devoted to the investigation of the effects of periodic drug treatment on a standard within-host virus model. We first introduce the basic reproduction ratio for the model, and then show that the infection free equilibrium is globally asymptotically stable, and the disease eventually disappears if $\mathcal{R}_{0} < 1$, while there exists at least one positive periodic state and the disease persists when $\mathcal{R}_{0}>1$. We also consider an optimization problem by shifting the phase of these drug efficacy functions. It turns out that shifting the phase can certainly affect the stability of the infection free steady state. A numerical study is performed to illustrate our analytic results. [ABSTRACT FROM AUTHOR]

Abstract: A cholera epidemic model with periodic transmission rate is presented. The basic reproduction number is defined. It is shown that the disease-free equilibrium is globally asymptotically stable and the cholera eventually disappears if the basic reproduction number is less than one. And if the basic reproduction number is greater than one, there exists a positive periodic solution which is globally asymptotically stable. Numerical simulations are provided to illustrate analytical results. [Copyright &y& Elsevier]

Abstract: This paper deals with the impulsive Lasota–Wazewska model with multiple time-varying delays. Our results show that the system is uniformly persistent under some appropriate conditions. The sufficient condition for global exponential stability of the system is given. Applying Mawhin’s continuation theorem of coincidence degree, we prove that the periodic system has at least one strictly positive periodic solution. By employing hull theory of impulsive almost periodic system, the existence and uniqueness of strictly positive almost periodic solution of the almost periodic system is obtained. Two examples are provided to illustrate our results. [Copyright &y& Elsevier]

Abstract: We study the internal structure of the global attractor of a uniformly persistent flow. We show that the restriction of the flow to the global attractor has duality properties which can be expressed in terms of certain attractor-repeller decompositions. We also study some natural Morse decompositions of the flow and calculate their Morse equations. These equations provide necessary and sufficient conditions for the existence of attractors with the shape of or such that their suspension has spherical shape. [Copyright &y& Elsevier]

Abstract: A mathematical model is formulated to describe the spread of hepatitis B. The stability of equilibria and persistence of disease are analyzed. The results shows that the dynamics of the model is completely determined by the basic reproductive number ρ 0. If ρ 0 <1, the disease-free equilibrium is globally stable. When ρ 0 >1, the disease-free equilibrium is unstable and the disease is uniformly persistent. Furthermore, under certain conditions, it is proved that the endemic equilibrium is globally attractive. Numerical simulations are conducted to demonstrate our theoretical results. The model is applied to HBV transmission in China. The parameter values of the model are estimated based on available HBV epidemic data in China. The simulation results matches the HBV epidemic data in China approximately. [Copyright &y& Elsevier]

In this study, we propose and investigate a two-stage population model with cannibalism. It is shown that cannibalism can destabilize and lower the magnitude of the interior steady state. However, it is proved that cannibalism has no effect on the persistence of the population. Based on this model, we study two systems of predator–prey interactions where the prey population is cannibalistic. A sufficient condition based on the nontrivial boundary steady state for which both populations can coexist is derived. It is found via numerical simulations that introduction of the predator population may either stabilize or destabilize the prey dynamics, depending on cannibalism coefficients and other vital parameters. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, we deal with a discrete predator–prey model with monotonic functional responses and give a sufficient condition of uniform persistence for the system. [Copyright &y& Elsevier]

In this paper, a periodic epidemic model with age structure in a patchy environment is introduced. We investigate its global dynamics in term of the basic reproduction number R0, and show that there exists at least one positive periodic state and the disease persists when R0 > 1 while the disease will die out if R0 < 1. Some numerical examples are given to confirm our analytic results and to show that the age and spatial heterogeneities are important factors for the global dynamics. [ABSTRACT FROM AUTHOR]

Infection caused by antibiotic-resistant pathogens is one of global public health problems. Many factors contribute to the emergence and spread of these pathogens. A model which describes the transmission dynamics of susceptible and resistant bacteria in a pregnant woman and the fetus is presented. Detailed qualitative analysis about positivity, boundedness, global stability and uniform persistence of the model is carried out. Numerical simulation and sensitivity analysis show that antibiotic input has potential impact for neonatal drug resistance. Our results show that the resistant bacteria in baby mainly come from antibiotics which are wrongly-used during gestational period, or foods containing antibiotic residues. [ABSTRACT FROM AUTHOR]

We analyse a selection-mutation size-structured model with n ecotypes competing for common resources. Uniform persistence and robust uniform persistence are established, when the selection-mutation matrix Γ is irreducible, i.e. individuals of one ecotype may contribute directly or indirectly to individuals of other ecotypes. Similar results are also presented for a particular reducible form of Γ. In the case of pure selection in which the offspring of one ecotype belong to the same ecotype, i.e. Γ=I, the identity matrix, we prove that the boundary equilibrium that describes competitive exclusion, with the fittest being the winner ecotype, is globally asymptotically stable. We show that small perturbations of the pure selection matrix lead to the existence of globally asymptotically stable interior equilibria. For the case when the selection-mutation matrix is reducible, we present and discuss the outcome of a series of numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the global dynamics of a viral infection model with a latent period. The model has a nonlinear function which denotes the incidence rate of the virus infection in vivo. The basic reproduction number of the virus is identified and it is shown that the uninfected equilibrium is globally asymptotically stable if the basic reproduction number is equal to or less than unity. Moreover, the virus and infected cells eventually persist and there exists a unique infected equilibrium which is globally asymptotically stable if the basic reproduction number is greater than unity. The basic reproduction number determines the equilibrium that is globally asymptotically stable, even if there is a time delay in the infection. [Copyright &y& Elsevier]

Abstract: The global stability of the endemic equilibrium is shown for an endemic model with infinite-dimensional population structure using a Volterra like Lyapunov function and the Krein–Rutman theorem. [Copyright &y& Elsevier]

Abstract: A two-species ratio-dependent predator–prey diffusion model with variable time delays is investigated. By constructing some suitable Lyapunov functionals and utilizing some analysis techniques, we obtain the permanence of this system. Our results generalize and improve the results of . [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the nonautonomous Lotka–Volterra system with dispersion. Under the assumption that the intrinsic growth rates of the species may be negative, we show that certain average conditions imply the uniform persistence of all species. Some known result is improved. [Copyright &y& Elsevier]

A West Nile epidemic model in discrete-time is proposed. The model consists of two interacting populations, the vector and the avian populations. The avian population is classified into susceptible, infective, and recovered classes while an individual vector is either susceptible or infective. The transmission of the disease is assumed only by mosquitoes bites and vertical transmission in the vector population. The model behavior depends on a lumped parameter R0. The disease-free equilibrium is locally asymptotically stable if R0 < 1. The system is uniformly persistent and possesses a unique endemic equilibrium if R0 > 1. Consequently, the disease can persist in the populations if R0 > 1. [ABSTRACT FROM AUTHOR]

A discrete hierarchical model with either age, size, or stage structure is derived. The resulting scalar equation for total population level is then used to study contest and scramble intra-specific competition. It is shown how equilibrium levels and resilience are related for the two different competition situations. In particular, scramble competition yields a higher population level while contest competition is more resilient if the uptake rate as a function of resource density is concave down. The conclusions are reversed if the uptake rate is concave up. [Copyright &y& Elsevier]

An autonomous SIRS epidemic model of two competitive species with interinfection of disease is formulated and analyzed. Some thresholds are identified and global asymptotic stability results of the bounded equilibria are proved. To the interior equilibrium, its local asymptotic stability is obtained. And under suitable conditions, it is proved that the model is uniformly persistent. Moreover, it is discovered that the interfinfection of disease is crucial to the dynamical behavior of the system, namely, when the two species coexist and the disease persists in both of them, and if the interinfection is removed, then three different cases may occur.

A mathematical model of microbial competition for limiting nutrients and for a limited set of available wall-attachment sites in an advection-dominated tubular reactor is formulated as a limiting case of the more general model considered in [M. Ballyk and H. L. Smith, A flow reactor with wall growth, in Mathematical Models in Medical and Health Sciences, M. Horn, G. Simonett, and G. Webb, eds., Vanderbilt University Press, Nashville, TN, 1998]. The model consists of a system of hyperbolic PDE. The existence and stability properties of its steady state solutions are investigated, both analytically and numerically. A surprising finding in the case of two-strain competition is the existence of a steady state solution characterized by the segregation of the two bacterial strains to separate nonoverlapping segments along the tubular reactor. [ABSTRACT FROM AUTHOR]

In this paper, we formulate and study a compartmental model for Lassa fever transmission dynamics considering human-to-human, rodent-to-human transmission and the vertical transmission of the virus in rodents. To incorporate the impact of periodicity of weather on the spread of Lassa, we introduce a non-autonomous model with time-dependent parameters for rodent birth rate and carrying capacity of the environment with respect to rodents. We introduce the basic reproduction number and show that it can be used as a threshold parameter concerning the global dynamics. It also shown that the disease-free periodic solution is globally asymptotically stable in the case of R 0 < 1 and if R 0 > 1 , then the disease persists. We show numerical studies for the Lassa fever in Nigeria and give examples to describe what kind of parameter changes might trigger the periodic recurrence of Lassa fever. [ABSTRACT FROM AUTHOR]