Modelling and stability analysis of SVEIRS yellow fever two host model

Kung’aro, Monica; Luboobi, Livingstone S.; Shahada, Francis

doi:10.56947/gjom.v3i3.152

Cited by 6 publications

(7 citation statements)

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“…Epidemiological modeling studies commonly assume that people from endemic communities are immune or vaccinated and symptomatic individuals do not travel ( 25 ). Migrants may not necessarily be from the endemic community, but they could have been exposed to the virus when passing through it and thus are more likely to be susceptible, acquiring and transmitting the disease.…”

Section: Discussionmentioning

confidence: 99%

Effects of migration rates and vaccination on the spread of yellow fever in Latin American communities

Simon

Amaku

Massad

2023

Revista Panamericana De Salud Pública

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Objective. To assess how relevant the flow of people between communities is, compared to vaccination and type of vector, on the spread and potential outbreaks of yellow fever in a disease-free host community. Methods. Using a SEIRV-SEI model for humans and vectors, we applied numerical simulations to the scenarios: (1) migration from an endemic community to a disease-free host community, comparing the performance of Haemagogus janthinomys and Aedes aegypti as vectors; (2) migration through a transit community located on a migratory route, where the disease is endemic, to a disease-free one; and (3) effects of different vaccination rates in the host community, considering the vaccination of migrants upon arrival. Results. Results show no remarkable differences between scenarios 1 and 2. The type of vector and vaccination coverage in the host community are more relevant for the occurrence of outbreaks than migration rates, with H. janthinomys being more effective than A. aegypti. Conclusions. With vaccination being more determinant for a potential outbreak than migration rates, vaccinating migrants on arrival may be one of the most effective measures against yellow fever. Furthermore, H. janthinomys is a more competent vector than A. aegypti at similar densities, but the presence of A. aegypti is a warning to maintain vaccination above recommended levels.

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Section: Discussionmentioning

confidence: 99%

Effects of migration rates and vaccination on the spread of yellow fever in Latin American communities

Simon

Amaku

Massad

2023

Revista Panamericana De Salud Pública

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“…negative, hence the first condition is satisfied (Kung'aro et al, 2015). By definition, the optimal solution u * i (t) ∈ R n is convex and bounded in U and thus the second condition is also satisfied (Collins et al, 2009;Mpeshe et al, 2014a;Mlay et al, 2015).…”

Section: Existence Of the Optimal Controlsmentioning

confidence: 98%

“…The Principle is used to obtain the differential equations for the adjoint variables, corresponding boundary conditions as well as the characterization of an optimal solution J (u * i ) for the optimal model (104). Characterization gives a representation of an optimal control in terms of state variables by minimizing the Hamiltonian, H (X, u, λ), with respect to the controls and the adjoint function (Namawejje et al, 2015;Kung'aro et al, 2015). To obtain the minimum Lagrangian of the optimal problem, we establish the Hamiltonian function H (X, u, λ), of the control problem with respect to its state variable X (t), control variable u (t) and the adjoint function λ (t) as follows:…”

Section: Characterization Of the Optimal Controlmentioning

confidence: 99%

Modeling the dynamics, control and economic loss of newcastle disease in village chicken: a case of Pwani region in Tanzania

Chuma¹

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Newcastle disease (ND) is a highly contagious viral bird disease affecting the domestic and other wild birds. The disease is a major threat to the farming of village chicken by small, medium, and large scale farmers. In this dissertation, a non-linear deterministic mathematical model of ND to study the dynamics, control and the economic loss of the village poultry with village chicken population, wild birds population of virus in the environment is formulated and analyzed. The basic reproduction number(R0) which represents the number of secondary cases where one case would produce in a completely susceptible population is derived using the Next Generation Matrix technique. The bifurcation analysis of the equilibrium points shows that a model exhibits the forward bifurcation meaning that the R0 less than a unit is a sufficient condition to reduce the transmission of ND in village chicken population. The sensitivity analysis of the parameters in R0 were computed using a normalized forward sensitivity analysis, results show that the transmission coefficient of the Newcastle disease virus between the hosts and the environment is found to be the most positive sensitive parameter in the model. A model is then extended to include three time dependent variables: vaccination, culling and the environmental hygiene and sanitation control strategies. To determine the best control strategy to mitigate the ND burden, the optimal control techniques are applied. The existence of the optimal control problem is proved with the necessary conditions for optimality determined using the Pontryagin’s Maximum Principle. Numerical simulations were performed using the forward-backward sweep iterative scheme of Runge-Kutta method of order four. Finally, a cost-effectiveness analysis is performed using the Incremental Cost-Effective Ratio (ICER). The results showed that the vaccination control strategy indicates the lowest cost compared to other control measures. The economic burden of the ND to chicken farmers, is considered as the total annual expenditure that a chicken farmer can incur to rescue the at risk chicken population from the ND is also investigated. The economic data of the model were collected from ten villages of Bagamoyo and Kibaha, Tanzania. Results from this study indicate that the recurrence of the ND in the village chicken population could lead to a serious economic loss at family level in this already financially constrained environment where small and medium farmers operate. The results obtained shows that there was 22:5% loss from their expected profit post Newcastle outbreaks in 2017. Also the results show that the occurrence of the ND leads to an average range of 482:89 􀀀 541:30$ economic loss at family in 2017. Therefore, for the effective control of NDV and its transmission we recommend vaccination to be paired with regular cleaning of chicken yards.

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“…We therefore take our strategies to be strategy A (personal protection only), strategy B (personal protection and spray of insecticides) and strategy C (personal protection, educational campaign combined with spray of insecticides) and the baseline option of no strategy (no control). Thus, based on the model simulation results of the paper titled Application of optimal control strategies for the dynamics of YF by Kung'aro et al (2015) [Chapter 4] we rank the strategies in order of increasing effectiveness as in Table 5.1. We assume that costs of personal protection and educational campaign are directed to all human population groups (i.e susceptible, vaccinated, exposed, infected and recovered), while spray of insecticide (which include larvicide and adulticide) costs will be directed to buying of the spraying medicine and paying the workers who engage on spraying activities for the aim of reducing vector population.…”

Section: Incremental Cost-effectiveness Ratiomentioning

confidence: 99%

Mathematical Modelling of Intra and Inter Dynamics and Control of Yellow Fever in Primate and Humna Populations

Kung’aro¹

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A deterministic mathematical model was formulated using non-linear ordinary differential equations to gain an insight of dynamics of yellow fever (YF) between primates, human beings and Aedes mosquito for the purpose of controlling the disease. Basic reproduction number, R0, was computed and its sensitivity analysis with respect to epidemiological parameters was performed to study the effect of model parameters to R0. Results showed that R0 is most sensitive to daily biting rate of mosquitoes, recruitment rate of vectors, probability of transmission of infection, recruitment of unvaccinated immigrants and the incubation period for both vector and humans. Thus, for the minimization of YF transmission, these parameters should closely be monitored. Stability analysis of disease-free equilibrium (DFE) and endemic equilibrium (EE) points were performed to study perseverance and conditionnecessaryfordiseaseinterruptionandcontrol. ResultsshowedthattheDFEislocally asymptotically stable if the rate of new infection from infected monkey to vector is less than unity, and is globally asymptotically stable if the rate of new infection from infected vector to human is less than unity. Lyapunov stability theory and LaSalles Invariant Principle were used to investigate stability of EE. Results show that EE is globally asymptotically stable whenever R0 > 1. To assess the impact of control measures on YF dynamics, we derived and analysed the necessary conditions for optimal control using optimal control theory. Results show that multipleoptimalcontrolstrategyisthemosteffectivetobringastabledisease-freeequilibrium compared to single and two controls. However, spray of insecticides alone was not effective without personal protection, and optimal use of personal protection alone is beneﬁcial to minimize transmission of the infection to the community. Furthermore, cost-effectiveness analysis of the optimal control measures was considered. We used incremental cost-effectiveness ratio to investigate and compare the costs required against the health beneﬁts achieved between two or more alternative intervention strategies that compete for the same resource. Results showed that combination of all strategies is the most cost-effective compared to others.

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Modelling and stability analysis of SVEIRS yellow fever two host model

Cited by 6 publications

References 0 publications

Effects of migration rates and vaccination on the spread of yellow fever in Latin American communities

Effects of migration rates and vaccination on the spread of yellow fever in Latin American communities

Modeling the dynamics, control and economic loss of newcastle disease in village chicken: a case of Pwani region in Tanzania

Mathematical Modelling of Intra and Inter Dynamics and Control of Yellow Fever in Primate and Humna Populations

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