Abstract
Objectives: While studies had established standard epidemic models, variants of those standards, which define unique and characteristic behavior of some of disease amidst interventions and population dynamics, are continually developed to represent epidemic dynamics in different ways. Methods: In this study, a compartmental susceptible-susceptible quarantine-vaccinated-exposed-quarantined-infectious-hospitalized-funeral-recovered (SSQVEQIHFR) epidemic model is formulated and analyzed. Model stability was analyzed and found to be both stable for disease-freeand endemic equilibrium. Findings: In order to determine its threshold (basic reproduction number), the next generation matrix approach was applied, and was found to represented average secondary transmissions of cases in the community, hospital and at funerals during the entire period of the epidemic. A numerical simulation was used to validate the disease-free and endemic equilibrium stability of the model. Applications: In order to determine influential parameters, a forward sensitivity index analysis was carried out on the model threshold and endemic points. This model has more classes which can be used to investigate infectious diseases outbreak with such characteristic dynamics. Preventive or control measures that averts transmission in the community, hospital and at funeral will stall the growth of epidemic in the population. Keywords: Epidemic Model, Reproduction Number, Sensitivity Analysis and Stability Model, Stability Analysis
Highlights
Epidemic models provide information that can help assess, predict and proffer optimal intervention control measures for stopping outbreaks
The study established the model stability at both disease-free and endemic equilibrium based on proven theorems of Jacobian and Lyapunov function construction
The model threshold reproduction number is determined using the generation approach, the threshold accounted for the contribution of new infection from the symptomatic class of the community (I), hospitalized (H) and dead individuals unsafely buried (F)
Summary
Epidemic models provide information that can help assess, predict and proffer optimal intervention control measures for stopping outbreaks. Infectious disease model becomes high-dimensioned if it includes compartments like alatent stage, vector-borne, pre-exposed immunity after recovery, infectious cadavers, asymptomatic infectious, disease-carrier individuals, transmission. These SEIR variants assessed theimpact of newer compartments of control or intervention, disease states or demography on the disease dynamics. In studies[3,6,7,14,15] it was noted that control measures, like contact tracing, quarantine and isolation, are commonly implemented to control outbreaks These intervention and control measures have been extensively implemented in epidemics like Measles, cholera, SARS Ebola, MERS, Zika virus etc. Safe burial controls Ebola virus disease and similar infectious diseases that cadavers can transmit virus The impact of this measure to widespread of the disease had been widely investigated[9,12]. The study of influential transmission or control parameters, parameter to incidences and prevalence of the disease in the population is carried out using sensitivity analysis of the reproduction number and endemic equilibrium points
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