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In this paper, we investigated a new heroin–cocaine epidemic model which incorporates spatial heterogeneity and nonlinear incidence rate. The main project of this paper is to explore the threshold dynamics in terms of the basic reproduction number $ \mathcal {R}_0 $ R 0 , which was defined by applying the next-generation operator. The threshold type results shown that if $ \mathcal {R}_0 \lt 1 $ R 0 < 1 , then the drug-free steady state is globally asymptotically stable. If $ \mathcal {R}_0 \gt 1 $ R 0 > 1 , then heroin–cocaine spread is uniformly persistent. Furthermore, the globally asymptotic stability of the drug-free steady state has been established for the critical case of $ \mathcal {R}_0=1 $ R 0 = 1 by analysing the local asymptotic stability and global attractivity. [ABSTRACT FROM AUTHOR]

This paper aims to apply an optimal control theory for the autonomous model of the leptospirosis epidemic to examine the effect of four time-dependent control measures on the model dynamics with cost-effectiveness. Pontryagin's Maximum Principle was used to derive the optimality system associated with the optimal control problem. Numerical simulations of the optimality system were performed for different control strategies and the results were presented graphically with and without controls. The optimality system was simulated using the Forward-Backward Sweep method in the Matlab programme. The numerical results revealed that the combination of all optimal control measures is the most effective strategy for minimizing the spread and impact of disease in the community. Furthermore, a cost-effectiveness analysis was performed to determine the most cost-effective strategy using the incremental cost-effectiveness ratio approach and we observed that the rodenticide control-only strategy is most effective to combat the spread of disease when available resources are limited.

In this paper, we are concerned with an epidemic model with quarantine and distributed time delay. We define the basic reproduction number R 0 and show that if R 0 ≤ 1 , then the disease-free equilibrium is globally asymptotically stable, whereas if R 0 > 1 , then it is unstable and there exists a unique endemic equilibrium. We obtain sufficient conditions for a Hopf bifurcation that induces a nontrivial periodic solution which represents recurrent epidemic waves. By numerical simulations, we illustrate stability and instability parameter regions. Our results suggest that the quarantine and time delay play important roles in the occurrence of recurrent epidemic waves.

In this paper, we consider the dynamical behaviour of a stochastic coronavirus (COVID-19) susceptible-infected-removed epidemic model with the inclusion of the influence of information intervention and Lévy noise. The existence and uniqueness of the model positive solution are proved. Then, we establish a stochastic threshold as a sufficient condition for the extinction and persistence in mean of the disease. Based on the available COVID-19 data, the parameters of the model were estimated and we fit the model with real statistics. Finally, numerical simulations are presented to support our theoretical results.

In this paper, a reaction-diffusion SIR epidemic model via environmental driven infection in heterogeneous space is proposed. To reflect the prevention and control measures of disease in allusion to the susceptible in the model, the nonlinear incidence function E f ( S ) is applied to describe the protective measures of susceptible. In the general spatially heterogeneous case of the model, the well-posedness of solutions is obtained. The basic reproduction number R 0 is calculated. When R 0 ≤ 1 the global asymptotical stability of the disease-free equilibrium is obtained, while when R 0 > 1 the model is uniformly persistent. Furthermore, in the spatially homogeneous case of the model, when R 0 > 1 the global asymptotic stability of the endemic equilibrium is obtained. Lastly, the numerical examples are enrolled to verify the open problems.

In this paper, we propose a model to assess the impacts of budget allocation for vaccination and awareness programs on the dynamics of infectious diseases. The budget allocation is assumed to follow logistic growth, and its per capita growth rate increases proportional to disease prevalence. An increment in per-capita growth rate of budget allocation due to increase in infected individuals after a threshold value leads to onset of limit cycle oscillations. Our results reveal that the epidemic potential can be reduced or even disease can be eradicated through vaccination of high quality and/or continuous propagation of awareness among the people in endemic zones. We extend the proposed model by incorporating a discrete time delay in the increment of budget allocation due to infected population in the region. We observe that multiple stability switches occur and the system becomes chaotic on gradual increase in the value of time delay.

Epidemiological models with the identical basic reproduction number R 0 may behave differently on both short time scale and long time scale. In this paper, we compare the predicted final sizes for several deterministic epidemic models and estimate the probabilities of a minor/major outbreak for continuous-time Markov chain (CTMC) models, all epidemic models have the identical R 0 . It is proved that the final size predicted by the epidemic model with homogeneous mixing is larger than with heterogeneous mixing. For CTMC models with heterogeneous mixing, the probabilities of a minor outbreak initiated by superspreaders and non-superspreaders are calculated and compared. For both deterministic modelling and stochastic modelling, numerical simulations are performed to support the mathematical analysis.

In this paper, we consider the impact of heterogeneous susceptibility on disease transmission dynamics, using a simple mathematical model formulated by a system of ordinary differential equations. Our model describes a time-varying immunity level, which is enhanced by reinfection and diminished by waning immunity. Through mathematical analysis, we show that unexpected outbreaks, called delayed outbreaks, occur even when the basic reproduction number is less than one. A reallocation of susceptibility at the individual level, by repeated infections, in the host population induces delayed outbreaks.

A delayed SEIR epidemic model with saturated incidence and saturated treatment function is considered in this paper. Sufficient conditions for the existence of local Hopf bifurcation are established by regarding the possible combination of the two delays as the bifurcation parameter. General formula for the direction, period and stability of the bifurcated periodic solutions are derived by using the normal form method and the centre manifold theory. Finally, some numerical simulations are given to illustrate the obtained results.

Scarlet fever is an acute respiratory infectious disease and the incidence rate is increasing from 2011 throughout the world. In this paper, the mathematical models are proposed, which incorporate both direct transmissions and indirect transmissions of scarlet fever. The threshold conditions for disease invasion are obtained in terms of the basic reproduction number. The peak value, final size and epidemic time in a seasonal prevalence are investigated numerically. Furthermore, the effects of seasonal fluctuations on disease outbreak are also studied on the basis of real data in China. [ABSTRACT FROM AUTHOR]

In meta-population models for infectious diseases, the basic reproduction number R 0 can be as much as 70% larger in the case of preferential mixing than that in homogeneous mixing [J.W. Glasser, Z. Feng, S.B. Omer, P.J. Smith, and L.E. Rodewald, The effect of heterogeneity in uptake of the measles, mumps, and rubella vaccine on the potential for outbreaks of measles: A modelling study , Lancet ID 16 (2016), pp. 599-605. doi: 10.1016/S1473-3099(16)00004-9 ]. This suggests that realistic mixing can be an important factor to consider in order for the models to provide a reliable assessment of intervention strategies. The influence of mixing is more significant when the population is highly heterogeneous. In this paper, another quantity, the final epidemic size ( F ) of an outbreak, is considered to examine the influence of mixing and population heterogeneity. Final size relation is derived for a meta-population model accounting for a general mixing. The results show that F can be influenced by the pattern of mixing in a significant way. Another interesting finding is that, heterogeneity in various sub-population characteristics may have the opposite effect on R 0 and F .

This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed stress-induced competition. When the disease is chronic, and the within-host dynamics are rapid, we reduce the partial differential equation model (PDE) to a three-dimensional ordinary differential equation (ODE) model. The ODE model exhibits backward bifurcation and sustained oscillations caused by the stress-induced competition. Furthermore, the ODE model, although not a special case of the PDE model, is useful for detecting backward bifurcation and oscillations in the PDE model. Backward bifurcation related to stress-induced competition allows the second species to persist for values of its invasion number below one. Furthermore, stress-induced competition leads to destabilization of the coexistence equilibrium and sustained oscillations in the PDE model. We suggest that complex systems such as this one may be studied by appropriately designed simple ODE models.

In this paper, an epidemiological model with age of infection and disease relapse is investigated. The basic reproduction number for the model is identified, and it is shown to be a sharp threshold to completely determine the global dynamics of the model. By analysing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By means of suitable Lyapunov functionals and LaSalle's invariance principle, it is verified that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable, and hence the disease dies out; if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable and the disease becomes endemic.

A new social epidemic model to depict alcoholism with media coverage is proposed in this paper. Some fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated. Stability of all equilibria are studied. The existence of the optimal control pair and mathematical expressions of optimal control are obtained by Pontryagin's maximum principle. Numerical simulations are also performed to illustrate our results. Our results show that media coverage is an effective measure to quit drinking.

In this paper, we introduce a basic reproduction number for a multi-group SIR model with general relapse distribution and nonlinear incidence rate. We find that basic reproduction number plays the role of a key threshold in establishing the global dynamics of the model. By means of appropriate Lyapunov functionals, a subtle grouping technique in estimating the derivatives of Lyapunov functionals guided by graph-theoretical approach and LaSalle invariance principle, it is proven that if it is less than or equal to one, the disease-free equilibrium is globally stable and the disease dies out; whereas if it is larger than one, some sufficient condition is obtained in ensuring that there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. Furthermore, our results suggest that general relapse distribution are not the reason of sustained oscillations. Biologically, our model might be realistic for sexually transmitted diseases, such as Herpes, Condyloma acuminatum, etc. [ABSTRACT FROM AUTHOR]

This article proposes a dispersal strategy for infected individuals in a spatial susceptible-infected-susceptible (SIS) epidemic model. The presence of spatial heterogeneity and the movement of individuals play crucial roles in determining the persistence and eradication of infectious diseases. To capture these dynamics, we introduce a moving strategy called risk-induced dispersal (RID) for infected individuals in a continuous-time patch model of the SIS epidemic. First, we establish a continuous-time n-patch model and verify that the RID strategy is an effective approach for attaining a disease-free state. This is substantiated through simulations conducted on 7-patch models and analytical results derived from 2-patch models. Second, we extend our analysis by adapting the patch model into a diffusive epidemic model. This extension allows us to explore further the impact of the RID movement strategy on disease transmission and control. We validate our results through simulations, which provide the effects of the RID dispersal strategy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that a large class of epidemic models, with both demography and non-permanent immunity incorporated in a rather general manner, can be mathematically formulated as a scalar renewal equation for the force of infection.

In this paper, the effect of a change in the distribution of age differences between sexual partners on the dynamics of the HIV epidemic is studied. In a gender- and age-structured compartmental model, it is shown that if the variance of the distribution is small enough, an increase in this variance strongly increases the basic reproduction number. Moreover, if the variance is large enough, the mean age difference barely affects the basic reproduction number. We, therefore, conclude that the local stability of the disease-free equilibrium relies more on the variance than on the mean.

The transmission of cholera involves both human-to-human and environment-to-human pathways that complicate its dynamics. In this paper, we present a new and unified deterministic model that incorporates a general incidence rate and a general formulation of the pathogen concentration to analyse the dynamics of cholera. Particularly, this work unifies many existing cholera models proposed by different authors. We conduct equilibrium analysis to carefully study the complex epidemic and endemic behaviour of the disease. Our results show that despite the incorporation of the environmental component, there exists a forward transcritical bifurcation at R (0)=1 for the combined human-environment epidemiological model under biologically reasonable conditions.

We deal with stochastic epidemic models having a set of absorbing states. The aim of the paper is to study some continuous characteristics of the epidemic. In this sense, we first extend the classical study of the length of an outbreak by investigating the whole probability distribution of the extinction time via Laplace transforms. Moreover, we also study two almost new epidemic descriptors, namely, the time until a non-infected individual becomes infected and the time until the individual is removed from the infective group. The obtained results are illustrated by numerical examples including an application to a stochastic SIS model for head lice infections.

We derive a stochastic epidemic model for the evolving density of infective individuals in a large population. Data shows main features of a typical epidemic consist of low periods interspersed with outbreaks of various intensities and duration. In our stochastic differential model, a novel reproductive term combines a factor expressing the recent notion of 'attenuated Allee effect' and a capacity factor is controlling the size of the process. Simulation of this model produces sample paths of the stochastic density of infectives, which behave much like long-time Covid-19 case data of recent years. Writing the process as a stochastic diffusion allows us to derive its stationary distribution, showing the relative time spent in low levels and in outbursts. Much of the behaviour of the density of infectives can be understood in terms of the interacting drift and diffusion coefficient processes, or, alternatively, in terms of the balance between noise level and the attenuation parameter of the Allee effect. Unexpected results involve the effect of increasing overall noise variance on the density of infectives, in particular on its level-crossing function. [ABSTRACT FROM AUTHOR]

A multi-patch HIV/AIDS model with heterosexual transmission is formulated to investigate the impact of population migration on the spread of HIV/AIDS. We derive the basic reproduction number $ R_{0} $ R 0 and prove that if $ R_{0} \lt 1 $ R 0 < 1 , the disease-free equilibrium is globally asymptotically stable. If $ R_{0} \gt 1 $ R 0 > 1 and certain conditions are satisfied, the endemic equilibrium is globally asymptotically stable. We apply the model to two patches and conduct numerical simulations. If HIV/AIDS becomes extinct in each patch when two patches are isolated, the disease remains extinct in two patches when the population migration occurs; if HIV/AIDS spreads in each patch when two patches are isolated, the disease remains persistent in two patches when the population migration occurs; if the disease disappears in one patch and spreads in the other patch when they are isolated, the disease can spread or disappear in two patches if migration rates of individuals are suitably chosen. [ABSTRACT FROM AUTHOR]

Many factors influencing disease transmission vary throughout and across populations. For diseases spread through multiple transmission pathways, sources of variation may affect each transmission pathway differently. In this paper we consider a disease that can be spread via direct and indirect transmission, such as the waterborne disease cholera. Specifically, we consider a system of multiple patches with direct transmission occurring entirely within patch and indirect transmission via a single shared water source. We investigate the effect of heterogeneity in dual transmission pathways on the spread of the disease. We first present a 2-patch model for which we examine the effect of variation in each pathway separately and propose a measure of heterogeneity that incorporates both transmission mechanisms and is predictive ofR0. We also explore how heterogeneity affects the final outbreak size and the efficacy of intervention measures. We conclude by extending several results to a more generaln-patch setting. [ABSTRACT FROM AUTHOR]

In this paper, we analyse the interaction of different species of birds and mosquitoes on the dynamics of West Nile virus (WNV) infection. We study the different transmission efficiencies of the vectors and birds and the impact on the possible outbreaks. We show that the basic reproductive number is the weighted mean of the basic reproductive number of each species, weighted by the relative abundance of its population in the location. These results suggest a possible explanation of why there are no outbreaks of WNV in Mexico. [ABSTRACT FROM PUBLISHER]

A deterministic model proposed in previous literatures to approximate the well-known Richards model is investigated. However, the model assumption of small initial value for infection size is released in the current manuscript. Taking the advantage of the closed form of solutions, we establish the epidemic characteristics of disease transmission: the outbreak size, the peak size and the turning point for the cumulative infected cases. It is shown that the usual disease outbreak threshold condition (the basic reproduction number R0 is greater than unity) fails to fully guarantee the existence of peaking time and turning point when the initial infection size is not relatively small. The epidemic characteristics not only depend on R0 but also on another index, the net reproduction number R*0. [ABSTRACT FROM AUTHOR]

A discrete-time deterministic epidemic model is proposed to better understand the contagious dynamics and the behaviour observed in the incidence of real infectious diseases. For this purpose, we analyse a SIRS model both in a random-mixing approach and in a small-world network formulation. The models include the basic parameters that characterize an epidemic: infection and recovery times, as well as mechanisms of contagion. Depending on the parameters, the random-mixing model has different types of behaviour of an epidemic: pathogen extinction; endemic infection; sustained oscillations and dynamic extinction. Spatial effects are included in our network-based approach, where each individual of a population is represented by a node of a small-world network. Our network-based approach includes rewiring connections to account for time-varying network structure, a consequence of the natural response to the emergence of an epidemic (e.g. avoiding contacts with infected individuals). Random and adaptive rewiring conditions are analysed and numerical simulation are made. A comparison of model predictions with the actual effects of COVID-19 infection on population that occurred in Italy and France is produced. Results of the time series of infected people show that our adaptive evolving networks represent effective strategies able to decrease the epidemic spreading. [ABSTRACT FROM AUTHOR]

In this article, a stochastic SACR hepatitis B epidemic model is taken to be under consideration. We develop a stochastic epidemic model by considering the effect of environmental fluctuation on the hepatitis B dynamics and distribute the transmission rate by white noise. Using the stochastic Lyapunov function theory, we have shown the existence and uniqueness of the global positive solution. The extinction and persistence for our proposed model are derived with sufficient conditions. The numerical simulations are carried out using first-order Itô-Taylor stochastic scheme in the last section for the verification of our theoretical results. [ABSTRACT FROM AUTHOR]

We model the extent to which age-targeted protective sequestration can be used to reduce ICU admissions caused by novel coronavirus COVID-19. Using demographic data from New Zealand, we demonstrate that lowering the age threshold to 50 years of age reduces ICU admissions drastically and show that for sufficiently strict isolation protocols, sequestering one-third of the countries population for a total of 8 months is sufficient to avoid overwhelming ICU capacity throughout the entire course of the epidemic. Similar results are expected to hold for other countries, though some minor adaption will be required based on local age demographics and hospital facilities. [ABSTRACT FROM AUTHOR]

Global eradication of Guinea worm disease (GWD) is in the final stage but a mysterious epidemic of the parasite in dog population makes the elimination programme challenging. There is neither a vaccine nor an effective treatment against the disease and therefore intervention strategies rely on the current epidemiological understandings to control the spread of the disease. A novel mathematical model can predict the future outbreaks and it can quantify the dissemination rates of control interventions. Due to the lack of such novel models, a realistic mathematical model of GWD dynamics with human population, dog population, copepod population and the worm larvae is proposed and analyzed. Considering case data from Chad, we calibrate the model and perform global sensitivity analysis of the basic reproduction number with respect to the control parameters and copepod consumption rates. Furthermore, we investigate the impact of three control interventions: awareness of humans, isolation of infected dogs and copepod clearance from contaminated water sources. We also address the impact of combination interventions which leads to the conclusion that the combination of isolating the infected dogs and treating the contaminated ponds is a plausible way for eliminating the burden of GWD from Chad. [ABSTRACT FROM AUTHOR]

We develop an age of infection model with heterogeneous mixing in which indirect pathogen transmission is considered as a good way to describe contact that is usually considered as direct and we also incorporate virus shedding as a function of age of infection. The simplest form of SIRP epidemic model is introduced and it serves as a basis for the age of infection model and a 2-patch SIRP model where the risk of infection is solely dependent on the residence times and other environmental factors. The computation of the basic reproduction number , the initial exponential growth rate and the final size relation is done and by mathematical analysis, we study the impact of patches connection and use the final size relation to analyse the ability of disease to invade over a short period of time. [ABSTRACT FROM AUTHOR]

The role of spatial arrangements on the spread and management strategies of a cholera epidemic is investigated. We consider the effect of human and pathogen movement on optimal vaccination strategies. A metapopulation model is used, incorporating a susceptible- infected-recovered system of differential equations coupled with an equation modelling the concentration of Vibrio cholerae in an aquatic reservoir. The model compared spatial arrangements and varying scenarios to draw conclusions on how to effectively manage outbreaks. The work is motivated by the 2010 cholera outbreak in Haiti. Results give guidance for vaccination strategies in response to an outbreak. [ABSTRACT FROM AUTHOR]

Crimean-Congo haemorrhagic fever (CCHF) is a highly contagious tick-borne disease that impacts many countries in parts of Africa, Europe, Asia, and the Middle East. Outbreaks are episodic, but deadly. Due to the highly contagious nature of this disease, suspected cases are taken extremely serious, with very strong control measures implemented almost immediately. It is primarily those living on farms, livestock workers, and medical workers who are at risk. The virus responsible for CCHF is transmitted asymptomatically and transiently to livestock, and symptomatically to humans. The fatality rate in human cases can be very high. The number of methods and directions of viral transmission is large, including tick-to-tick, tick-to-livestock, tick-to-human, livestock-to-tick, livestock-to-human, and human-to-human. We model CCHF using a deterministic system of nonlinear differential equations. This compartment model allows us to analyse threshold parameters and equilibria describing the magnitude and progression of cases of the disease in a hypothetical outbreak. [ABSTRACT FROM AUTHOR]

We describe a new approach for investigating the control strategies of compartmental disease transmission models. The method rests on the construction of various alternative next-generation matrices, and makes use of the type reproduction number and the target reproduction number. A general metapopulation SIRS (susceptible--infected--recovered--susceptible) model is given to illustrate the application of the method. Such model is useful to study a wide variety of diseases where the population is distributed over geographically separated regions. Considering various control measures such as vaccination, social distancing, and travel restrictions, the procedure allows us to precisely describe in terms of the model parameters, how control methods should be implemented in the SIRS model to ensure disease elimination. In particular, we characterize cases where changing only the travel rates between the regions is sufficient to prevent an outbreak. [ABSTRACT FROM AUTHOR]

For wildlife species living among patchy habitats, disease and the Allee effect (reduced per capita birth rates at low population densities) may together drive a patch's population to extinction, particularly if births are seasonal. Yet local extinction may not be indicative of global extinction, and a patch may become recolonized by migrating individuals. We introduce deterministic and stochastic susceptible, infectious, and immune epidemic models with vector species to study disease in a metapopulation with an Allee effect and seasonal birth and dispersal. We obtain conditions for the existence of a strong Allee effect and existence and stability of a disease-free positive periodic solution. These general models have application to many wildlife diseases. As a case study, we apply them to evaluate dynamics of the sylvatic plague in prairie dog colonies interconnected through dispersal. We further evaluate the effects of control of the vector population and control by immunization on plague eradication. [ABSTRACT FROM AUTHOR]

In this work, we propose novel epidemic models (named, susceptible-infected-recovered-susceptiblebacteria) for cholera dynamics by incorporating a general formulation of bacteria growth and spatial variation. In the first part, a generalized ordinary differential equation (ODE) model is presented and it is found that bacterial growth contributes to the increase in the basic reproduction number, R0. With the derived basic reproduction number, we analyse the local and global dynamics of the model. Particularly, we give a rigorous proof on the endemic global stability by employing the geometric approach. In the second part, we extend the ODE model to a partial differential equation (PDE) model with the inclusion of diffusion to capture the movement of human hosts and bacteria in a heterogeneous environment. The disease threshold of this PDE model is studied again by using the basic reproduction number. The results on the threshold dynamics of the ODE and PDE models are compared, and verified through numerical simulation. Additionally, our analysis shows that incorporating diffusive spatial spread does not produce a Turing instability when R0 associated with the ODE model is less than the unity. [ABSTRACT FROM AUTHOR]

We study a susceptible.infected.susceptible model with distributed delays. By constructing suitable Lyapunov functionals, we demonstrate that the global dynamics of this model is fully determined by the basic reproductive ratio R0. To be specific, we prove that if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. On the other hand, if R0 > 1, then the endemic equilibrium is globally asymptotically stable. It is remarkable that the model dynamics is independent of the probability of immunity lost. [ABSTRACT FROM AUTHOR]

We formulate a deterministic epidemic model for the spread of Hepatitis C containing an acute, chronic and isolation class and analyse the effects of the isolation class on the transmission dynamics of the disease. We calculate the basic reproduction numberR0and show that forR0≤1, the disease-free equilibrium is globally asymptotically stable. In addition, it is shown that for a special case whenR0>1, the endemic equilibrium is locally asymptotically stable. Furthermore, an analogous stochastic epidemic model for Hepatitis C is formulated using a continuous time Markov chain. Numerical simulations are used to estimate the mean, variance and probability distributions of the discrete random variables and these are compared to the steady-state solutions of the deterministic model. Finally, the expected time to disease extinction is estimated for the stochastic model and the impact of isolation on the time to extinction is explored. [ABSTRACT FROM AUTHOR]

We investigate the time evolution of disease spread on a network and present an analytical framework using the concept of disease generation time. Assuming a susceptible–infected–recovered epidemic process, this network-based framework enables us to calculate in detail the number of links (edges) within the network that are capable of producing new infectious nodes (individuals), the number of links that are not transmitting the infection further (non-transmitting links), as well as the number of contacts that individuals have with their neighbours (also known as degree distribution) within each epidemiological class, for each generation period. Using several examples, we demonstrate very good agreement between our analytical calculations and the results of computer simulations. [ABSTRACT FROM AUTHOR]

The emergence and spread of drug resistance is one of the most challenging public health issues in the treatment of some infectious diseases. The objective of this work is to investigate whether the effect of resistance can be contained through a time-dependent treatment strategy during the epidemic subject to an isoperimetric constraint. We apply control theory to a population dynamical model of influenza infection with drug-sensitive and drug-resistant strains, and solve the associated control problem to find the optimal treatment profile that minimizes the cumulative number of infections (i.e. the epidemic final size). We consider the problem under the assumption of limited drug stockpile and show that as the size of stockpile increases, a longer delay in start of treatment is required to minimize the total number of infections. Our findings show that the amount of drugs used to minimize the total number of infections depends on the rate ofde novoresistance regardless of the initial size of drug stockpile. We demonstrate that both the rate of resistance emergence and the relative transmissibility of the resistant strain play important roles in determining the optimal timing and level of treatment profile. [ABSTRACT FROM AUTHOR]

We describe a multiple strain Susceptible Infected Recovered deterministic model for the spread of an influenza subtype within a population. The model incorporates appearance of new strains due to antigenic drift, and partial immunity to reinfection with related circulating strains. It also includes optional seasonal forcing of the transmission rate of the virus, which allows for comparison between temperate zones and the tropics. Our model is capable of reproducing observed qualitative patterns such as the overall annual outbreaks in the temperate region, a reduced magnitude and an increased frequency of outbreaks in the tropics, and the herald wave phenomenon. Our approach to modelling antigenic drift is novel and further modifications of this model may help improve the understanding of complex influenza dynamics. [ABSTRACT FROM AUTHOR]

We present two ordinary differential equation models for Rift Valley fever (RVF) transmission in cattle and mosquitoes. We extend existing models for vector-borne diseases to include an asymptomatic host class and vertical transmission in vectors. We define the basic reproductive number,0, and analyse the existence and stability of equilibrium points. We compute sensitivity indices of0and a reactivity index (that measures epidemicity) to parameters for baseline wet and dry season values.0is most sensitive to the mosquito biting and death rates. The reactivity index is most sensitive to the mosquito biting rate and the infectivity of hosts to vectors. Numerical simulations show that even with low equilibrium prevalence, increases in mosquito densities through higher rainfall, in the presence of vertical transmission, can result in large epidemics. This suggests that vertical transmission is an important factor in the size and persistence of RVF epidemics. [ABSTRACT FROM AUTHOR]