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MODELING SEASONALITY IN AVIAN INFLUENZA H5N1

The number of cases of H5N1 avian influenza in birds and humans exhibit seasonality which peaks during the winter months. What causes the seasonality in H5N1 cases is still being investigated. This article addresses the question of modeling the periodicity in cumulative number of human cases of H5N1. Three potential drivers of influenza seasonality are investigated: (1) seasonality in bird-to-bird transmission; (2) seasonality caused by wild bird migration or seasonal fluctuation of avian influenza in wild birds; (3) seasonality caused by environmental transmission. A framework of seven models is composed. The seven models involve these three mechanisms and combinations of the mechanisms. Each of the models in the framework is fitted to the cumulative number of humans cases of H5N1. The corrected akaike information criterion (AICc) is used to compare the models and it is found that the model with periodic bird-to-bird transmission rate best explains the data. The best fitted model with the best fitted parameters gives a reproduction number of highly pathogenic avian influenza . The best fitted model is a simple SI epidemic model with periodic transmission rate and disease-induced mortality, however, this model is capable of very complex dynamical behavior such as period doubling and chaos.

Optimal control of a malaria model with asymptomatic class and superinfection

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, R0, is computed using the next generation approach. The system has a disease-free equilibrium (DFE) which is locally asymptomatically stable when R0<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.

On the principle of host evolution in host–pathogen interactions

ABSTRACT In this paper, we use a two-host one pathogen immuno-epidemiological model to argue that the principle for host evolution, when the host is subjected to a fatal disease, is minimization of the case fatality proportion . This principle is valid whether the disease is chronic or leads to recovery. In the case of continuum of hosts, stratified by their immune response stimulation rate a, we suggest that has a minimum because a trade-off exists between virulence to the host induced by the pathogen and virulence induced by the immune response. We find that the minimization of the case fatality proportion is an evolutionary stable strategy for the host.

Vector-Borne Pathogen and Host Evolution in a Structured Immuno-Epidemiological System.

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

Effect of air travel on the spread of an avian influenza pandemic to the United States

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Structural and Practical Identifiability Analysis of Zika Epidemiological Models

R0 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

Structural and Practical Identifiability Issues of Immuno-Epidemiological Vector–Host Models with Application to Rift Valley Fever

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